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Quiz

Lesson 1 – Rate of Change and Differentiation Rules — Picture questions (exam style)

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  • Questions count: 300
  • Passing grade: 60%
Start Quiz
1.
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 = 2
a = 2, b = 2
a = 2, b = -2
a = 1, b = -2
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 = -2 or 1, sum of k = 2
k = -2 or -1, sum of k = -2
k = -2 or -1, sum of k = -3
k = 1 or 2, sum of k = 3
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)).
16
15
-15
5.881
4.
Using the table, find (ef)′ at x = 2.
Using the table, find (e^f)′ at x = 2.
-2.718
-1
2.718
0.3679
5.
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 = -1, b = -1
a = -1, b = 1
a = -1, b = -2
a = 0, b = -2
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)).
-0.181
1.814
-0.725
0.725
7.
Find the gradient of the tangent to the curve shown at the 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
0
6
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)).
0.052
2.472
-0.105
0.105
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 = -3, b = -4
a = -2, b = 3
a = -3, b = 3
a = -3, b = -3
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)).
0.5
1.5
0
1
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)).
0.785
5.302
-1.06
-5.302
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)).
21.136
5.284
-21.136
-0.268
13.
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 = -4, b = 4
a = 4, b = -2
a = -4, b = 2
a = 4, b = -3
14.
Find the gradient of the tangent to the curve shown at the 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
7
5
2.5
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)).
-4.092
-12.277
12.277
-6.672
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)).
-4.5
4
4.5
1.5
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)).
1
-3
1.571
3
18.
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 = -2
a = 2, b = 2
a = -2, b = -2
a = -1, b = -3
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)).
7.549
4.274
17.098
-17.098
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)).
-0.964
1.08
0.964
0.241
21.
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 = -2
a = -2, b = 4
a = -2, b = -4
a = 2, b = 4
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)).
5.581
8
-8
2.667
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)).
-3
3
0
1.5
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)).
-1.168
1.168
-0.779
-0.234
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)).
2.773
0.5
1
0
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)).
-1.95
-2.115
5.851
-5.851
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)).
-34.903
34.903
12.961
6.981
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)).
0.865
-0.865
1.028
0.173
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)).
-2.5
0
-5
5
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)).
-0.541
-0.021
2.164
-2.164
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)).
10.963
-10.963
-3.654
1.118
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)).
-3
0
-0.75
3
33.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
2.216
4
5
-4
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)).
28.299
-28.299
10.204
5.66
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)).
1.118
-1.118
1.228
0.373
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)).
2.1
10.828
4.2
-4.2
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)).
1.732
-1.732
0.866
0.75
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)).
4.258
-5.286
5.286
1.057
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)).
5.44
-5.44
-1.088
1.839
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)).
8.438
2.6
1.3
-2.6
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)).
5
1
0
0.5
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)).
-4.667
11.493
4.667
5.667
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)).
-1
1
-0.161
-0.25
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)).
-14.617
-8.745
-4.872
14.617
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)).
3.5
0.7
-3.5
6.375
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)).
0.541
0.271
-0.135
-0.271
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)).
7
-3.785
-3.5
-7
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)).
-1.13
1.13
0.283
0.543
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)).
0.595
1.23
0.41
-1.23
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)).
3.676
-14.702
7.23
14.702
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)).
-1.394
-1.111
-6.968
6.968
52.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.362
0.181
0.362
-1.814
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)).
2.246
-4.492
1.732
4.492
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)).
9.667
4.458
3.222
-9.667
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)).
-1.755
-2.755
-0.719
2.755
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)).
0.919
-5.683
6.683
5.683
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)).
1.774
-4.149
4.149
-2.074
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)).
-3.893
4.893
3.893
2.468
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
-2
0.667
6.047
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)).
0.081
-0.161
0.161
0.683
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)).
0.5
-1
0
1
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)).
-5.415
3.452
-2.707
5.415
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)).
-1.237
4.946
-4.946
-3.297
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)).
-6
6
0
-1.5
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)).
-0.725
3.628
0.725
-0.362
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)).
3.992
-0.179
-3.992
-1.331
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)).
-12.487
12.487
-3.122
-2.048
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)).
1
2
0.5
0
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)).
22.167
-11.084
-22.167
-20.167
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)).
-2
-1.5
-3
3
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)).
0.917
2.75
-2.75
3.386
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)).
-3.644
3.644
6.719
4.644
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)).
4
-4
0
1
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)).
-7
7
3.215
8
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)).
0
-1
0.2
1
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)).
4.21
-3.21
3.21
4.42
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)).
-9.668
-4.193
2.417
9.668
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)).
-1.361
1.361
6.119
0.34
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)).
-4.274
4.274
-1.069
-0.082
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)).
0.333
1.333
-0.333
0.416
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)).
2.857
-2.857
-0.952
-7.892
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)).
1.25
-0.417
-3.159
-1.25
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)).
5
-5
-1.25
2.356
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)).
-0.96
-3.558
0.96
-0.32
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)).
1.353
4.521
-2.705
2.705
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)).
6.27
5.922
-5.922
2.961
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)).
4.438
-1.883
5.438
-4.438
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)).
7.274
0.308
1.308
-0.308
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)).
-0.311
1.499
0.311
-0.078
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)).
-3.102
4.102
1.551
3.102
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)).
0.758
3.033
1.516
-1.516
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)).
0
-7
3.5
7
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)).
-0.083
-4.592
0.333
-0.333
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)).
5.81
0.98
-0.98
0.245
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)).
-0.047
2
-0.667
-2
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)).
1.5
3.464
1.732
-3.464
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)).
2.287
3.756
4.756
-3.756
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)).
-4.222
1.056
4.222
14.986
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)).
-7
7
4.874
8
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)).
0.333
-1
1
0
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)).
0.53
-1.076
0.215
1.076
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)).
2
3.48
-2
3
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)).
1.829
-9.143
7.264
9.143
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)).
3.878
1.479
-2.878
2.878
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)).
-6.844
6.844
1.711
1.27
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)).
-7.915
1.146
1.979
7.915
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)).
-9
-4.511
9
-4.5
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)).
-1.793
5.702
1.793
2.793
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)).
-2.495
-0.475
-1.424
1.424
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)).
13
0
-13
-2.6
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)).
-12
12
2.4
-1.37
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)).
-0.541
0.27
0.541
-5.961
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)).
5.064
2.532
-5.064
7.064
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)).
-3
0
0.75
3
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)).
-1.718
-2.968
11.872
-11.872
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)).
6
1.37
1.2
-6
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)).
-0.564
0.141
0.564
0.62
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)).
0.363
1.363
2.335
-0.363
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)).
3.6
10.438
1.8
-3.6
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)).
4.511
-4.714
4.714
0.943
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)).
3.307
3.027
-3.027
-2.027
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)).
-14
14
-3.5
0
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)).
6.931
0
0.5
1
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)).
2.272
1.272
-1.272
2.752
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
-1.5
-7.5
7.5
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)).
-9
10
-10
-5.558
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)).
-1.226
1.226
0.566
0.409
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)).
2.249
-2.6
0.867
2.6
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)).
1.149
-2.298
1.046
2.298
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)).
1.918
-0.919
-0.184
0.919
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)).
4.818
0.964
15.592
-4.818
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)).
-16.857
-3.784
-4.214
16.857
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)).
0.245
-0.245
0.061
1.453
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)).
-0.471
0.118
0.471
2.894
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)).
-0.748
-2.243
2.243
2.985
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)).
2.09
-10.452
10.452
1.666
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)).
3.667
-3.667
4.099
1.833
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)).
21.651
-21.651
1.25
-4.33
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)).
-0.963
-0.115
-3.851
3.851
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)).
-9.745
5.496
3.248
9.745
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)).
-3.027
0.827
-0.757
3.027
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)).
11
-11
0
3.667
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)).
4.728
3.248
-9.456
9.456
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)).
-0.1
-3.375
0.5
-0.5
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)).
2.5
5
0
-5
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)).
-0.434
1.303
-3.857
-1.303
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)).
0.952
2.857
9.73
-2.857
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)).
0.382
1.174
-1.146
1.146
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)).
1
0.5
-2.197
0
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)).
5.718
2.359
-1.359
1.359
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)).
1.814
5.921
-5.921
1.48
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)).
0
0.5
-4.159
1
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)).
3.219
-1.073
0.156
-3.219
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)).
-0.617
-5.571
5.571
-2.785
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)).
6
-6
1.2
0
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)).
2.336
1.226
-9.345
9.345
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)).
-11.391
11.391
7.088
2.278
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)).
3.858
-7.716
5.303
7.716
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)).
0.524
5.936
-0.131
-0.524
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)).
1.193
4.471
-0.894
-4.471
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)).
30.416
13.708
68.541
-68.541
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)).
-3.193
12.849
-2.57
-12.849
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)).
1
2.207
0.5
0
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)).
-4.189
-3.193
4.189
-1.396
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)).
13.591
27.183
-27.183
28.183
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)).
4.006
1.171
5.857
-5.857
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)).
-4.349
-0.274
13.047
-13.047
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
1
0.5
0
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)).
6.514
-1.644
0.411
1.644
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)).
-91.369
18.274
91.369
34.547
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)).
-12.177
2.435
12.177
-1.504
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)).
0.041
1.041
2.005
-0.041
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)).
3
-2
1.386
2
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)).
-44.334
23.167
11.084
44.334
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)).
-3.207
3.202
-6.415
6.415
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)).
2.667
-0.533
-2.667
-4.584
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)).
-6.928
6.928
1.732
1.5
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)).
-7.994
1.998
7.994
-1.228
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)).
1.889
-6.394
-1.889
-0.472
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)).
7
5.901
-7
-1.75
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)).
0.69
3.524
-2.524
2.524
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)).
1.801
-1.801
-2.886
-0.9
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)).
0.5
-3
1
0
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)).
1.728
-6.994
6.994
-1.748
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)).
-1.225
1.225
0.408
0.919
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)).
0.528
1.303
-0.303
0.303
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)).
-0.586
0.414
0.586
-0.157
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)).
0.5
-1
1.5
-1.5
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)).
4.429
2.753
0.886
-4.429
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)).
3.081
-3.683
-3.081
-2.081
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)).
5.551
4.551
4.29
-4.551
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)).
17.452
-17.452
-3.49
-7.981
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)).
-3.784
4.134
7.568
-7.568
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)).
1
0
-2
2
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)).
-0.159
0.46
-0.46
0.54
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)).
1.654
3.027
-3.027
-1.514
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)).
-0.308
0.103
0.308
1.179
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)).
5.658
0.282
-1.886
-5.658
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)).
0.358
0.098
-0.098
0.024
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)).
0.884
0.514
-2.572
2.572
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)).
-3.2
3.2
-1.6
-8.828
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)).
-0.323
5
-2.5
-5
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)).
-10.075
24.734
-6.183
-24.734
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)).
0.5
3
-3
-1
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)).
-12.962
-2.592
-3.506
12.962
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)).
-1.224
4.895
-2.139
-4.895
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)).
8.333
-8.333
9.333
3.88
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)).
2.594
1.594
1.414
-1.594
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)).
3.645
-6.5
6.5
-1.3
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)).
-4.851
4.851
5.851
1.115
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)).
-1.189
-1.75
-7
7
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)).
1.379
9.524
-8.524
8.524
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)).
-6.439
6.439
0.312
-2.146
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)).
-0.909
-0.039
-0.154
0.154
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)).
3
-3
0
-1
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)).
7.5
8.338
-15
15
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)).
-0.593
1.597
-0.597
-1.597
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)).
-12
12
4
0
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)).
1.842
3.286
0.921
-1.842
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)).
-2.207
2.207
-0.997
-0.736
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)).
-2.237
3.237
0.79
2.237
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
0.333
0.524
1
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)).
-0.921
0.46
1.643
0.921
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)).
2.809
0.598
-2.809
-0.562
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)).
8.191
2.73
8.801
-8.191
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)).
35.739
-7.148
-35.739
-4.352
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)).
0.403
10.896
-10.896
2.179
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)).
3.732
-8.492
1.698
8.492
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)).
-2.794
-27.408
9.136
27.408
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)).
5.6
1.867
-5.6
3.749
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)).
3.336
1.558
-2.336
2.336
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)).
-4.056
-2.291
11.453
-11.453
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)).
-9.248
10.728
-10.728
-9.728
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)).
-8.658
2.637
8.658
-2.165
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)).
0.861
0.269
1.076
-1.076
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)).
0.919
-0.919
10.546
1.919
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)).
-1.4
1.4
1.333
0.467
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)).
2.568
8.136
3.568
-2.568
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)).
-3.371
-6.743
-3.027
6.743
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)).
3.122
2
-4
4
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)).
-29.416
-68.541
-13.708
68.541
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)).
2
0.362
1
-1
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)).
6
-6
1.5
4.296
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)).
-0.386
0.5
1
0
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)).
-4.571
8
-8
-4
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)).
-0.702
-0.14
-0.454
0.702
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)).
-10
-2.5
10
0
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)).
-0.5
0.504
0.5
-0.87
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)).
1.857
-1.857
5.892
0.619
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)).
-7.761
3.441
7.761
2.587
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)).
1.5
1.785
-3
3
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)).
-1.551
-0.87
0.5
-0.5
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)).
3.5
-14
7.291
14
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)).
-0.1
-0.2
-2.828
0.2
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)).
-0.122
0.878
0.122
-0.021
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)).
-0.256
-1.28
1.28
-4.839
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)).
-1.832
-0.181
1.832
-0.832
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)).
-8
-2.667
0
8
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)).
-3.545
-1.678
-14.179
14.179
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)).
-0.459
0.459
0.092
-0.959
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)).
-0.07
0.35
1.357
-0.35
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)).
-1.429
1
3
-3
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)).
-0.462
-7.977
7.977
2.659
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)).
-2.193
-4.387
4.387
-3.387
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)).
-3.628
7.008
-7.008
1.402
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)).
4.755
1.959
3.755
-3.755
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)).
-1.718
2.718
-2.718
-4.437
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)).
-18
4.5
18
0
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)).
0.3
1.2
4.828
-1.2
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)).
9.167
5.333
-5.333
1.067
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)).
-1
-6
2
6
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)).
-1.801
2.886
0.9
1.801
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)).
11
2.2
-11
4.149
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)).
3.456
-3.456
1.728
0.248
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)).
-10
1.571
10
-2.5
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)).
3
-6
0
6
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)).
-0.548
11.094
-3.698
-11.094
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)).
0.667
2
4.545
-2
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)).
-1.683
-1.764
-2.764
2.764
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)).
0.017
0.367
-0.004
-0.017
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)).
-10
2.5
10
8
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)).
0.65
1.65
-0.701
-0.65
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)).
1.262
4.145
2.073
-4.145
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)).
3.962
-2.962
2.962
3.924
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)).
-2.997
-1.997
2.997
-2.221
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)).
3.036
-15.178
15.178
-0.865
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)).
-2.047
-3.047
3.19
3.047
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)).
-1.73
3.459
-9.961
-3.459
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)).
-1.168
0.234
0.779
1.168
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)).
-3
3
-1
-5.22
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
0.5
4.159
0
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)).
1.25
-5
9.047
5
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)).
-0.367
0.062
1.367
0.367
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)).
0.931
-0.847
0.169
0.847
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)).
-15.31
-28.379
16.31
-16.31
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)).
-6.75
2.25
6.75
9.931
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)).
0.133
-0.667
3.584
0.667
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)).
3.881
-11.642
11.642
5.162
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)).
5.196
-5.196
2.25
-2.598
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)).
2.6
-1.6
3.219
1.6
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