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Quiz

Lesson 1: Differentiation of Trigonometric, Exponential and Logarithmic Functions — Picture questions (exam style)

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  • Questions count: 300
  • Passing grade: 60%
Start Quiz
1.
f(x) = 3 a⋅x + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
f(x) = 3 a⋅x + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
a = 3, b = -2
a = -1, b = -2
a = -2, b = 3
a = -2, b = -3
2.
If y = ekx satisfies the equation shown for all x, which option is correct?
If y = e^{kx} satisfies the equation shown for all x, which option is correct?
k = -1 or 2, sum of k = 2
k = -1 or 2, sum of k = -1
k = -2 or 1, sum of k = -2
k = -1 or 2, sum of k = 1
3.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.26
1.082
-1.082
2.082
4.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-38.171
60.257
-60.257
-20.086
5.
Using the table, find (ln f)′ at x = 1.
Using the table, find (ln f)′ at x = 1.
-3
0.3333
-1.099
-0.3333
6.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.571
1.047
0.785
-1.571
7.
f(x) = x 2 a⋅ℯ + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
f(x) = x 2 a⋅ℯ + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
a = 2, b = -4
a = 2, b = -3
a = -3, b = 3
a = -2, b = -4
8.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.833
-0.133
0.4
-0.4
9.
f(x) = a⋅sin(x) + b⋅cos(x) with constants a, b satisfies the two conditions shown. Which option is correct?
f(x) = a⋅sin(x) + b⋅cos(x) with constants a, b satisfies the two conditions shown. Which option is correct?
a = -1, b = -2
a = 2, b = -2
a = -1, b = 2
a = -1, b = 1
10.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.014
-5.071
5.071
-0.157
11.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4
-5
-2.785
5
12.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.999
-0.999
1.999
0.74
13.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-9.023
-3.097
9.023
-4.511
14.
f(x) = x 2 a⋅ℯ + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
f(x) = x 2 a⋅ℯ + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
a = -3, b = -2
a = 2, b = 3
a = 3, b = 2
a = 2, b = -2
15.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4
4
-3
0
16.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.809
0.562
-0.598
-2.809
17.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.364
2.364
9.194
0.473
18.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.5
-1.5
-6.238
-0.375
19.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.273
1.612
-2.273
0.568
20.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.388
1.897
3.388
-3.388
21.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.779
1.168
-0.292
-1.168
22.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.998
-1.481
-1.998
-0.998
23.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-8.155
11.155
4.077
8.155
24.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.995
-2.985
2.985
0.891
25.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.35
1.357
-0.07
-0.35
26.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-8.667
8.667
3.934
2.167
27.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.25
-5.196
2.598
5.196
28.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-8
8
-1.6
0
29.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-16.445
-1.676
5.482
16.445
30.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
6.928
3.464
-6.928
3
31.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.857
-0.371
-2.006
1.857
32.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1
0.5
0
0.693
33.
f(x) = x 2 a⋅ℯ + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
f(x) = x 2 a⋅ℯ + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
a = 1, b = 3
a = 2, b = -3
a = 1, b = 1
a = 1, b = -3
34.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-6.283
6.283
0
2.094
35.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.078
-0.311
0.311
1.499
36.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3
0.75
3
1.208
37.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-11.456
5.728
11.456
4.248
38.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.637
2.832
-3.637
4.637
39.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
8
-2
-8
-4.571
40.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.22
-0.073
1.771
0.22
41.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2
4
-4
5
42.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.918
0.24
-0.918
1.918
43.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-22
7.333
22
10.755
44.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.851
-5.851
5.851
-2.115
45.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.705
-3.705
4.705
1.059
46.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.764
1.683
3.764
2.764
47.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.374
1.374
0.275
7.231
48.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-6
-1.5
6
0
49.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.943
-0.961
-1.943
1.943
50.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-24.167
22.167
-22.167
-11.084
51.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.676
0.559
-1.676
-0.04
52.
f(x) = 3 a⋅x + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
f(x) = 3 a⋅x + b⋅x with constants a, b satisfies the two conditions shown. Which option is correct?
a = 3, b = 1
a = 3, b = -1
a = -3, b = 1
a = 1, b = -1
53.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3
1
0
-3
54.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
8.931
-5.75
5.75
1.917
55.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
12.438
4.6
2.3
-4.6
56.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.186
-0.32
0.107
0.32
57.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3.628
-7.008
1.402
7.008
58.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.75
4.931
0.583
-1.75
59.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.083
-8.333
8.333
5.894
60.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.755
-0.245
0.245
-0.041
61.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.57
1.13
-1.13
0.282
62.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3.851
-4.851
4.851
-1.115
63.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.6
0.867
2.6
2.249
64.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3
0.75
0
-3
65.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.597
1.597
-0.593
-1.597
66.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.5
4
0
1
67.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.02
5.987
-3.061
3.061
68.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.596
0.596
4.988
0.119
69.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-16.675
4.169
1.79
16.675
70.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0
1
1.5
0.5
71.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
5.323
6.046
-5.323
-1.331
72.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
5.764
-6.143
1.229
6.143
73.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1
-2
2
-2.779
74.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.222
0.056
6.986
-0.222
75.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
742.066
-742.066
-148.413
-297.826
76.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.979
1.146
-3.957
3.957
77.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.5
1
0
-2.197
78.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.737
0.579
-1.737
5.142
79.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.333
4.333
2.167
6.493
80.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.676
-1.676
-0.559
0.04
81.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.333
0.267
6.592
-1.333
82.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3.307
0.514
2.054
-2.054
83.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.203
0.406
-0.406
-0.812
84.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.889
-0.178
0.889
-4.394
85.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-6.329
6.329
-0.319
1.582
86.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
102.811
-42.125
-102.811
-20.562
87.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
21.225
7.653
-21.225
7.075
88.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
5
5.571
10
-10
89.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.827
-5.482
-0.559
5.482
90.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.597
-4.597
5.597
2.093
91.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-5
2.256
2.5
5
92.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
371.033
1855.164
-1855.164
740.066
93.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1
-1
-0.333
0.476
94.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-11
0
-3.667
11
95.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-35.621
-7.124
-16.248
35.621
96.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.687
-0.687
0.137
3.615
97.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.331
-3.992
-0.179
3.992
98.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.752
6.728
1.752
-0.752
99.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.606
-1.152
3.915
4.606
100.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.178
-6.606
6.606
3.303
101.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.418
0.041
0.484
2.418
102.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
17
-17
-3.4
0
103.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.5
3
1
0
104.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
6.595
9.595
3.297
-6.595
105.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
8.047
2
0.5
-2
106.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.65
0.65
1.65
3.299
107.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.073
-3.219
3.219
-0.156
108.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.667
-0.667
1.667
-2.901
109.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1
0.25
0
1
110.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.918
4.918
-2.459
-2.041
111.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.575
0.788
1.575
1.462
112.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.118
-1.118
0.373
1.228
113.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
6.723
7.482
-6.723
2.241
114.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0
2
-1
1
115.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.2
0
-1
1
116.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.584
6.909
2.584
-2.584
117.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
6.903
0.224
1.119
-1.119
118.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.382
1.174
1.146
-1.146
119.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.356
-11
11
2.75
120.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
6
-6
0
2
121.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.139
-0.895
-0.179
0.895
122.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.143
-2.591
2.591
0.864
123.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
10.91
1.577
-10.91
3.637
124.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0
17
4.25
-17
125.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2
-2
1
1.193
126.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.324
2.547
-1.547
-2.547
127.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0
7
-7
8
128.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3
0.5
0
1
129.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-5.584
3.667
-3.667
-0.733
130.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3.258
-3.286
-0.657
3.286
131.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.785
-1.25
5
-5
132.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1
-1
6.047
0.5
133.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0
5
0.5
1
134.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
10.873
-2.175
-10.873
-18.919
135.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3
0
-3
-1
136.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.822
-1.953
5.858
-5.858
137.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
13.017
-13.017
-1.295
2.603
138.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.73
0.243
-1.97
-0.73
139.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.571
3
1
-3
140.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.959
-0.959
1.959
1.505
141.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.5
1
1.472
0
142.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0
7
2.333
-7
143.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.481
1.998
2.998
-1.998
144.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1
-0.2
-5.375
-1
145.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-9.129
9.129
-1.826
-0.592
146.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.5
1.732
8.66
-8.66
147.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
6
1.5
-6
3.826
148.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
10.873
5.437
18.919
-10.873
149.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0
4.667
-14
14
150.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-5.256
5.256
-1.051
2.721
151.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.19
0.952
8.291
-0.952
152.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-5
0
5
1.667
153.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
8.851
4.115
7.851
-7.851
154.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.308
-4.886
-1.233
1.233
155.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1
0.5
0
1
156.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.787
8.935
-8.935
-1.088
157.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3.577
1.01
1.192
3.577
158.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.444
0.889
-0.889
-1.622
159.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.284
-3.568
-1.284
1.284
160.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.386
0.5
1
0
161.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.753
2.429
0.486
-2.429
162.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-13.486
-3.371
13.486
-3.027
163.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2
2
0.5
8.318
164.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.167
-1.773
0.5
-0.5
165.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.637
-0.819
0.168
-1.637
166.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.589
0.255
-1.021
1.021
167.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
6.054
-6.054
3.307
-3.027
168.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.568
-2.568
2.568
8.136
169.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.254
1.441
-6.761
6.761
170.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
18.678
-18.678
-4.321
-3.736
171.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.728
-2.728
-2.124
2.728
172.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.393
2.617
-1.571
1.571
173.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.838
-0.06
-2.515
2.515
174.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1
2
1.773
1
175.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-11.642
5.162
3.881
11.642
176.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.25
-2.215
5
-5
177.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.379
-1.895
-0.639
1.895
178.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3.296
0.5
1
0
179.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-5.558
6.558
3.628
5.558
180.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.076
-3.316
-0.381
0.381
181.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.056
-0.28
1.726
0.28
182.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.162
-1.054
-3.162
-3.04
183.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.559
3.452
0.559
0.112
184.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.061
0.82
-0.82
0.164
185.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
11.959
-7.167
1.433
7.167
186.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-13.708
68.541
-68.541
-26.416
187.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
73.891
110.836
-110.836
55.418
188.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.08
-0.964
0.241
0.964
189.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-5.115
-2.95
8.851
-8.851
190.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.75
0
-15
15
191.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.86
-0.785
-1.86
2.86
192.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.893
2.468
-3.893
4.893
193.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.532
5.064
-3.064
-5.064
194.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.222
0.444
10.986
2.222
195.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.857
1.857
2.006
0.371
196.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.828
-1.2
1.2
0.3
197.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.464
1
3.464
-3.464
198.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3
-2
-3
-3.826
199.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.117
-2.117
0.706
4.975
200.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
17.242
9.621
28.863
-28.863
201.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.472
0
1
0.5
202.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.929
-3.929
2.648
-0.786
203.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-10
-9
10
-5.558
204.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.715
14.144
0.706
-14.144
205.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.303
-0.434
-3.857
-1.303
206.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1
-0.25
0
-1
207.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.728
6.994
-6.994
-1.748
208.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.492
4.492
1.732
1.123
209.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.087
3.957
0.349
-0.349
210.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.014
-10.071
3.77
10.071
211.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.122
9.244
5.122
4.122
212.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
5.272
-6.752
-4.272
-5.272
213.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.949
1.949
-1.949
5.898
214.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.667
1.84
4.667
2.333
215.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.266
-1.33
2.071
1.33
216.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-13.486
13.486
-6.743
-6.054
217.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-6
-2.779
6
-1.5
218.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.598
12.99
-12.99
2.25
219.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0
9.425
-9.425
2.356
220.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.076
-1.076
0.861
0.269
221.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.341
-0.176
-0.706
0.706
222.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.333
-1.429
-4
4
223.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.844
3.306
-2.306
2.306
224.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
11.592
0.564
2.818
-2.818
225.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.166
0.83
-0.83
1.068
226.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.54
-9.093
9.093
4.546
227.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.5
0
-1.296
1
228.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.429
0.617
-2.215
-4.429
229.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.847
0.847
-0.423
-0.931
230.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.333
2.202
-4.667
4.667
231.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.667
-0.667
0.333
1.099
232.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.5
-1.307
1.5
-1.5
233.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.644
18.88
3.776
-18.88
234.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.851
-4.851
1.115
0.97
235.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.886
-0.282
-5.658
5.658
236.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1
1
0.5
-2.215
237.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
58.912
-152.281
152.281
30.456
238.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.946
-4.946
-3.297
-3.946
239.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.795
-2.297
0.459
2.297
240.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.333
-2.433
-0.667
1.333
241.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-15
8.338
15
16
242.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
7.985
1.597
2.102
-7.985
243.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.108
-0.133
0.667
-0.667
244.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.866
-3.866
2.071
3.866
245.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.617
-0.215
0.429
-0.429
246.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.865
1.028
0.173
-0.865
247.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.5
0
1
-1.104
248.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.847
1.99
0.847
0.282
249.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
18.473
73.891
35.945
-73.891
250.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
5.23
-12.702
12.702
6.351
251.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.169
-2.721
-4.169
-3.169
252.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.979
3.915
-3.915
-3.709
253.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.215
-3
1
3
254.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.117
7.41
-1.482
-7.41
255.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-13.601
13.601
-2.72
4.598
256.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
12.962
-4.321
0.854
-12.962
257.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.75
-0.866
-1.732
1.732
258.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
5.144
-3.536
-1.029
-5.144
259.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.838
1.613
-4.838
4.96
260.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.907
0.181
-0.181
-0.091
261.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-5.677
-6.677
6.677
2.302
262.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4.387
-2.193
-5.387
-4.387
263.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
3.059
0.17
0.68
-0.68
264.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.906
-0.226
2.267
0.906
265.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.822
-0.822
0.242
1.822
266.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
12.702
4.234
-12.702
7.468
267.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.732
-1.732
-2.732
-1.524
268.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
5.652
1.691
3.382
-3.382
269.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
11.5
11.802
-23
23
270.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
4
-6
1.5
6
271.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-5.819
1.168
-1.168
-0.168
272.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.886
-0.5
1
-1
273.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.5
-3.464
-1.732
3.464
274.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1
0
0.736
0.5
275.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3.957
-0.349
0.349
0.087
276.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
12.458
-3.115
-12.458
-5.027
277.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-29.556
-11.084
-44.334
44.334
278.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.649
-0.297
-0.649
-1.649
279.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.5
-6
6
0
280.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.215
0.555
1.073
-1.073
281.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.159
0.083
-0.25
0.25
282.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
6.119
-1.361
0.34
1.361
283.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.353
2.261
1.353
0.676
284.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2.221
-13.936
-2.787
13.936
285.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.551
0.47
-1.411
1.411
286.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
14.321
-2.864
-14.321
3.571
287.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
7.394
2.833
-5.667
5.667
288.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.909
-0.584
1.584
0.584
289.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.895
4.895
-0.979
-2.139
290.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.444
0.444
0.222
0.811
291.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.333
-0.595
1.333
-0.333
292.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-2
2
-1
1
293.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3.637
-0.154
0.846
0.154
294.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.792
-0.667
0.667
0.333
295.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
1.046
3.298
2.298
-2.298
296.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-1.636
0.327
-1.194
1.636
297.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
0.68
-3.059
-0.68
-0.17
298.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-3.011
-2.582
2.582
-0.646
299.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-4.946
1.649
4.946
3.297
300.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-7.5
6
7.5
1.5
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