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Quiz

Lesson 2 – Rules of Differentiation, Chain Rule and Tangent Lines — Picture questions (exam style)

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  • Questions count: 300
  • Passing grade: 60%
Start Quiz
1.
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 = 4, b = 4
a = -4, b = 3
a = 5, b = 4
a = 5, 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 = -3 or 2, sum of k = -1
k = -3 or 2, sum of k = 0
k = -3 or -2, sum of k = 0
k = -2 or 3, 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)).
-1
3.142
3
-3
4.
Using the table, find (f·g)′ at x = 1.
Using the table, find (f·g)′ at x = 1.
4
3
-8
-6
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 = 2, b = 2
a = 3, b = 1
a = 1, b = 0
a = 2, b = 1
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)).
3.215
-7
7
3.5
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 = 3, b = 3
a = 3, b = 4
a = 4, b = 3
a = 4, 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)).
0.1
-0.4
0.4
2.828
9.
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
Find the gradient of the tangent to the curve shown at the marked point (i.e. f′(x₀)).
-0.385
0.385
9.093
1.385
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)).
7
3.5
0
-7
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)).
-0.093
0.597
-0.597
0.403
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)).
7
-2.417
-1.4
-7
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)).
1.889
-5.667
2.725
5.667
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)).
-0.865
1.028
0.173
0.865
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)).
-0.137
-3.615
0.687
-0.687
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)).
0.541
1.245
-1.245
2.245
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)).
0.972
-0.972
0.48
1.972
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)).
4.482
7.963
13.445
-13.445
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)).
-6
6
4
1.5
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)).
0.048
-1.892
-0.143
0.143
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 = 3
a = 3, b = 2
a = 2, b = 2
a = -1, b = 3
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)).
-8.851
8.851
5.115
1.77
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)).
14.88
-14.88
0.644
2.976
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)).
-3.628
-2.96
11.842
-11.842
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)).
1.827
-0.559
-5.482
5.482
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)).
0.5
0
1
1.5
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)).
33.613
-33.613
8.403
13.445
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)).
1
0.5
-5
5
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)).
4.145
2.073
1.262
-4.145
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)).
2
1.571
-2
1
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)).
-3.985
-0.797
-1.102
3.985
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
-2
2
0
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)).
-0.045
0.453
0.181
-0.181
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)).
27.768
-5.554
-10.107
-27.768
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)).
7.263
0.306
1.225
-1.225
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)).
0
5
0.5
1
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)).
4.426
-4.426
5.426
2.557
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)).
10.873
7.249
21.746
-21.746
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)).
-0.584
0.584
0.389
1.584
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)).
1.924
1.201
0.6
-1.201
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)).
0.32
-0.96
3.558
0.96
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)).
-3.957
3.957
0.989
0.573
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)).
4.496
3.248
9.745
-9.745
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)).
15.082
-15.082
1.039
3.77
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)).
2.211
8.844
3.27
-8.844
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)).
2.915
-1.915
-2.915
-1.441
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)).
2
-0.667
-3.047
-2
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)).
1.612
3.273
2.273
-2.273
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)).
1.61
4.829
-4.829
-0.234
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)).
2.688
-1.688
2.376
1.688
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)).
-0.762
-2.286
-7.838
2.286
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)).
-3
-1.716
-2
3
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)).
3.5
-14
14
0
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)).
-5.921
1.48
1.814
5.921
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)).
0.717
0.616
-1.435
1.435
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)).
-8.844
-2.211
8.844
-3.27
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)).
0.149
12.384
-2.477
-12.384
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)).
6.796
-1.909
0.382
1.909
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)).
-7.148
35.739
-4.352
-35.739
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)).
2.402
-4.858
4.858
5.858
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)).
2.27
-4.541
4.541
-2.48
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)).
4.2
-21
21
0
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)).
7.44
5.22
4.22
-4.22
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)).
-401.711
698.977
401.711
200.855
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)).
2.779
5
-5
2.5
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)).
1
0.5
0.785
-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)).
2
-1.386
-2
-1
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)).
1.219
0.2
-0.2
-0.1
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)).
0
-2.773
0.5
1
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)).
15.136
-15.136
-3.784
4.134
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)).
6.559
2.761
-0.92
-2.761
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)).
-3.102
4.102
3.102
1.551
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)).
4.049
-1.871
2.024
-4.049
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)).
0.381
0.076
-0.381
3.316
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)).
-0.82
0.82
-0.41
-1.061
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)).
0.083
-0.017
1.837
-0.083
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)).
0.181
-0.363
0.363
1.168
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)).
-2
3
-3
0
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)).
-0.833
2.5
-2.5
-3.773
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)).
0.029
-1.006
0.143
-0.143
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)).
0.452
4.834
1.208
-4.834
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)).
1.174
-1.146
0.382
1.146
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)).
9
0
4.5
-9
84.
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 = 1
a = 1, b = 1
a = 1, b = 2
a = 2, b = 1
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)).
1.857
-1.857
0.371
2.006
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)).
-1.688
-3.376
3.376
-2.376
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)).
0.95
3.8
4.609
-3.8
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)).
1.125
0.233
-0.931
0.931
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)).
-4
3.142
2
4
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
-0.6
0
3
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)).
0.596
-0.596
0.119
4.988
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)).
-1.335
9.637
2.335
1.335
93.
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 = -3, b = 2
a = -3, b = -2
a = 3, b = 2
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)).
3.692
11.076
-11.076
3.972
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)).
1.514
6.743
-6.743
1.686
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)).
3.197
-4.667
4.667
1.167
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)).
0.583
-1.75
1.75
4.931
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)).
5.558
-5.558
-4.558
0.903
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)).
-0.161
0.5
1
-1
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)).
-0.017
0.367
0.017
-0.006
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)).
1.262
-1.262
0.555
2.262
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)).
0.444
0.222
0.811
-0.444
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)).
-8.851
-4.426
-5.115
8.851
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)).
0.964
0.241
1.08
-0.964
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)).
3.445
-7.832
7.832
2.611
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)).
-89.052
33.621
17.81
89.052
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)).
-1.118
1.228
1.118
0.373
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)).
5.785
-11
5.5
11
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)).
-5.922
6.27
5.922
2.961
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)).
19.787
4.947
2.864
-19.787
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)).
-0.282
-1.241
0.564
-0.564
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)).
55.418
-110.836
110.836
73.891
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)).
0.82
0.41
1.061
-0.82
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)).
1.97
-1.97
-0.657
1.141
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)).
-3
3
-1.5
-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)).
-2
-5.296
-1
2
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)).
3.854
-0.043
0.011
0.043
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)).
-15
15
5
0
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)).
3.49
0.151
-0.151
-0.05
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)).
0.149
0.046
-0.298
0.298
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)).
-0.667
0.133
0.667
3.584
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)).
0
0.5
-1.472
1
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)).
3.29
4.58
9.87
-9.87
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)).
-3.996
3.996
2.961
4.996
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)).
-5.895
5.895
2.639
1.179
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)).
-2.8
14
0
-14
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)).
-4
-2
0
4
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)).
1.073
0.555
-1.073
0.215
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)).
8.493
-6.333
6.333
3.167
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
0
2
-2
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)).
-9.425
2.356
9.425
0
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)).
0.5
0
1
3.296
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)).
-2
3
-1.5
-3
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)).
0.385
0.193
-0.385
4.546
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)).
-3.664
18.321
-18.321
1.476
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)).
-0.719
-3.597
-1.593
3.597
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)).
6.514
1.644
0.411
-1.644
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)).
-0.159
0.647
-0.216
-0.647
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)).
-0.544
2.721
-0.272
0.544
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)).
-20.168
-6.723
20.168
-14.445
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)).
-7
-1.4
0
7
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)).
0.735
-0.033
0.033
0.967
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)).
-7.5
-4
-1.5
7.5
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)).
6.672
3.069
-12.277
12.277
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)).
0.5
2
0
-2
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)).
-0.122
0.878
0.122
-0.021
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
-0.571
1
0.5
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)).
4.492
5.492
1.732
-4.492
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)).
-9.5
9.5
-1.9
0.504
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)).
1.25
9.047
5
-5
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)).
10.88
3.678
-2.176
-10.88
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)).
-2.207
0.5
0
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)).
-0.399
-0.593
-1.597
1.597
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)).
8.968
0.313
-1.254
1.254
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)).
3.773
-2.5
2.5
0.833
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)).
-8.155
16.31
-16.31
-5.437
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)).
-3.833
0.767
4.792
3.833
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)).
0.564
1.693
3.98
-1.693
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)).
2.047
-1.332
-6.66
6.66
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)).
1.732
0.75
-1.732
-0.866
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)).
1.084
3.909
-2.168
2.168
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)).
-1
0
0.25
1
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)).
-2.115
-5.851
5.851
-2.926
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
-1.396
-4.189
-5.193
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)).
1.801
-1.801
-2.886
-0.9
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)).
17
-0.785
-17
-4.25
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)).
3.244
-1.778
1.778
0.889
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)).
-8.773
8.773
4.387
10.773
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)).
1.654
6.054
-6.054
-1.514
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)).
0.282
-5.658
5.658
-1.886
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)).
-8.985
0.609
8.985
2.995
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)).
-1.382
-2.764
-0.841
2.764
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)).
-2.779
2.779
0.907
1.39
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)).
-0.478
6.947
-1.91
1.91
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)).
4.024
8.049
-0.871
-8.049
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
-0.333
0.356
-1
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)).
7.42
2.568
-6.42
6.42
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)).
-4.73
-23.651
23.651
1.453
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)).
6.56
13.678
-6.56
1.312
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)).
0.394
-1.111
1.111
-0.278
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)).
3.621
1.476
-1.476
2.476
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)).
0.716
-9.589
-1.918
9.589
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)).
-0.294
0.294
1.294
1.074
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
0
-1
0.333
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)).
-120.513
241.026
-241.026
-80.342
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)).
1.346
7.027
1.757
-7.027
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)).
0.368
-1.838
-3.836
1.838
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)).
2.75
-2.75
3.386
0.917
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
-5
2.5
0
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)).
-2.718
-2.437
-10.873
10.873
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)).
-1.998
2.998
1.998
1.481
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)).
1.213
0.607
-0.607
0.202
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)).
-0.257
-1.286
1.286
-2.258
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)).
5.667
2.202
-4.667
4.667
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)).
0.311
1.499
-0.078
-0.311
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)).
-11.277
-2.255
-5.672
11.277
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)).
-0.5
2.079
0.5
0.125
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)).
7.216
-28.863
28.863
17.431
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)).
-3.702
18.512
-9.405
-18.512
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)).
0.047
1.047
-0.047
2.006
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)).
4.414
-4.414
1.995
1.471
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)).
2.115
6.851
5.851
-5.851
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)).
2
0
-2
0.4
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)).
4.946
-1.649
-0.989
-4.946
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)).
2.6
-1.6
3.219
1.6
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)).
0.667
-1.333
3.493
1.333
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)).
-44.334
44.334
-8.867
-29.556
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
-1
5.558
2
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)).
-6.283
0
6.283
-1.571
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)).
-35.621
35.621
-7.124
-12.248
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)).
-0.46
0.54
0.46
-0.159
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)).
-0.35
1.357
-0.07
0.35
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)).
-0.607
1.055
0.607
0.152
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)).
-5.2
1.3
8.438
5.2
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)).
7.069
1.047
-1.414
-7.069
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)).
6.598
5.598
-5.598
3.071
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)).
-0.785
-5.302
1.06
5.302
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)).
3.916
-3.916
0.783
1.148
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)).
-11
0
2.2
11
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)).
-1.143
1.143
-0.381
-3.892
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)).
0
3.667
-11
11
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)).
-3.992
3.992
-1.331
-0.179
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)).
-1.299
1.299
1.599
2.299
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)).
-25
5
25
2.5
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)).
-1
1
0.2
0
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)).
-1.226
0.409
1.226
0.566
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)).
-3.705
7.41
-2.117
-7.41
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)).
-18.029
3.992
18.029
-3.606
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)).
-1.129
0.564
1.129
2.481
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)).
2.139
0.979
-4.895
4.895
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)).
-0.073
0.22
1.771
-0.22
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)).
9.136
-27.408
27.408
-2.794
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)).
-0.838
0.838
0.02
-0.279
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)).
-73.891
39.945
73.891
18.473
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)).
-13.607
4.478
13.607
2.721
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
0
-1
0.5
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)).
10.787
-20.128
21.128
20.128
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)).
-0.453
0.547
2.872
0.453
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)).
1113.099
-444.239
-222.62
-1113.099
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)).
4.5
-4.5
6.425
5.5
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)).
-6
-1.5
0.685
6
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)).
0.8
-0.8
0.223
1.8
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)).
-5.819
4.832
5.819
6.819
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)).
2
-2
-1
-3.48
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)).
-0.959
1.959
-1.959
1.505
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)).
37.1
-37.1
-15.113
-18.55
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)).
-2
1.047
0.667
2
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)).
-10.549
-8.549
8.549
-4.274
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)).
-8
8
4
0
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)).
-3.333
3.333
8.959
1.667
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)).
-3.826
-6
-1.5
6
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
0.5
1
0.736
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)).
0
-7
7
2.333
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)).
19.242
-4.81
-10.621
-19.242
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)).
-4.795
-23.973
23.973
1.791
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)).
0.898
-0.843
-4.213
4.213
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)).
-14
2.8
14
0
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)).
2.094
-8
2.667
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)).
0.457
2.758
-2.286
2.286
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)).
-2.222
1.111
2.222
4.055
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)).
4.23
11.702
-11.702
5.851
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)).
-11.586
-2.317
11.586
0.368
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)).
-2.429
4.858
1.234
-4.858
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)).
0.215
1
-1
0.333
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)).
0.524
-0.524
-0.131
5.936
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)).
-0.993
0.993
0.827
0.199
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)).
-4.591
4.591
5.591
1.199
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)).
0.423
1.27
2.985
-1.27
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)).
5
2.5
3
-5
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)).
-2.221
-2.997
-1.997
2.997
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)).
-5.482
-16.445
16.445
1.676
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)).
61.834
20.611
-61.834
25.188
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)).
-1.571
1.571
1.047
0.785
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)).
-6.283
-2.094
0
6.283
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)).
5.255
-5.255
1.051
-1.877
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)).
1
0.5
3
0
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)).
42.603
81.205
-81.205
20.301
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)).
3.466
-5
5
6
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)).
0.615
-0.615
-2.357
-0.205
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)).
10.452
-2.09
-1.666
-10.452
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)).
8.229
2.057
-8.229
4.514
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)).
3.454
-3.454
5.919
4.454
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)).
6.283
-6.283
0
2.094
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)).
-10.896
2.179
0.403
10.896
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)).
3.306
0.844
2.306
-2.306
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)).
0.105
-0.105
0.052
2.472
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)).
1.814
-0.725
0.725
-0.181
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
0.5
0
4
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)).
21.225
-20.225
-7.653
-21.225
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
-1.208
-3
-2
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)).
0.274
-13.953
13.953
-4.651
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)).
-1.6
1.6
-0.6
-0.446
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)).
-3.756
2.287
3.756
4.756
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)).
1.501
3.001
-3.001
4.81
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)).
-4
4
-1.333
0
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)).
-4.534
1.752
8.76
-8.76
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)).
-3
0
1.5
3
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)).
-0.308
0.308
3.637
0.154
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)).
-3.027
-6.743
6.743
-3.371
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)).
2.919
5.106
-4.106
-5.106
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