AP Calculus BC Unit 2 — Differentiation ‒ Definition and Basic Derivative Rules Practice Test
AP Calculus BC Unit 2 — Differentiation ‒ Definition and Basic Derivative Rules Practice Test
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Question 1 of 19
1. Question
Calculate the derivative of f ( x )=4 x^{ 2} −x+ 2 at the point x=1
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Question 2 of 19
2. Question
Evaluate the first derivative if f ( x )=2 e^{x} and x=0 .
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Question 3 of 19
3. Question
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Question 4 of 19
4. Question
Find the derivative of y=co s ^{−1} ( x ) +cos (x) .
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Question 5 of 19
5. Question
f ( x )=7 x ^{2} +6 x−9 . Give f ‘ (x) .
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Question 6 of 19
6. Question
What is the rate of change of the function f ( x )=1+3 x +3 x^{ 4} at the point (1,6) ?
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Question 7 of 19
7. Question
f ( x )=0.9 x ^{4} +0.7 x ^{3} −0.5 x . Give f ‘ ‘ ( x) .
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Question 8 of 19
8. Question
Give the second derivative of x ^{777} .
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Question 9 of 19
9. Question
Given the graph below, estimate g ‘(2) .
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Question 10 of 19
10. Question
The tangent line to the graph of function the point (7,6) . Find f ‘ (2) .
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Question 11 of 19
11. Question
Function h is graphed. The graph has a vertical tangent at x=−4 . Select all the x values for which h x=−4 . is not differentiable. Choose all answers that apply:
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Question 12 of 19
12. Question
Is the function given below continuous/differentiable at ?
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Question 13 of 19
13. Question
Noah tried to find the derivative of using basic differentiation rules. Here is his work: At which step did Noah make a mistake, if at all?
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Question 14 of 19
14. Question
The following table lists the value of functions and , and of their derivatives, and , for .Evaluate at .
Evaluate at
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Question 15 of 19
15. Question
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Question 16 of 19
16. Question
What is the equation of the line tangent to the graph h ( x )=−x 4 +6 x ^{2 }at the point where x=2
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Question 17 of 19
17. Question
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Question 18 of 19
18. Question
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Question 19 of 19
19. Question
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