Calculus AP



AP Calculus AB Name _____________________________

Derivative Review

In 1 – 12, Find the derivative of each function of x (assume y is a function of x).

1. [pic] 2. [pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic]

7. [pic] 8. [pic]

9. [pic] 10. [pic]

11. [pic] 12. [pic]

13. Find all points on the graph of [pic] whose tangent lines are parallel to the line 2x – 3y = 12.

14. Find the equation of the tangent line to [pic] at the point (1, –1).

15. Use logarithmic differentiation to find [pic]: [pic]

16. Find all points on the graph of [pic] at which there is a horizontal tangent line.

17. Determine whether the slope at the indicated point is

positive, negative or zero.

18 Use the graph to determine all x-values at which the function is NOT differentiable.

a) a, b, c, d, e, f, and g

b) b and d

c) a and f

d) a, f, and g

e) None of these

In 19 & 20, [pic]:

19. [pic] 20. [pic]

In 21 – 23, Given the following information, find the derivatives indicated:

|x |f (x) |f ' (x) |g(x) |g ' (x) |

|2 |5 |–1 |3 |2 |

|3 |6 |2 |–2 |–4 |

|5 |–3 |4 |5 |–1 |

[pic]

[pic]

[pic]

21. Find h'(2) 22. Find m'(2) 23. Find n'(2)

24. A coin is dropped from a height of 750 feet. The height, s (measured in feet), at time, t (measured in seconds), is given by [pic].

a) Find the average velocity on the interval [1, 3].

b) Find the instantaneous velocity when t = 3.

c) Find the acceleration at t = 2.

d) How long does it take the coin to hit the ground?

e) Find the velocity of the coin when it hits the ground.

f) On what time interval(s) is the coin speeding up or slowing down? Explain.

25. For each graph of a function below, sketch the graph of its derivative on the same axes.

a) b)

c) d)

26. The position of a car is given by the values in the following table. Estimate the instantaneous velocity when t = 2 seconds. Show how you got your answer.

|t(seconds) |0 |1 |2 |3 |4 |5 |

|s(feet) |0 |19 |38 |76 |128 |173 |

27. a) If an arrow is shot upward on the moon, with a velocity of 70 m/s, its height (in meters) after t seconds is given by [pic]. With what velocity will the arrow hit the moon?

b) What was the average velocity of the arrow between 35 and 45 seconds?

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e

f

g

x

y

x

y

d

c

b

a

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