1. Derivative
Practice
Family of f:
f & f’ & f’’
Definition
Of the
Derivative
Applied
Derivatives
NO Calc
Applied
Derivatives
WITH Calc
100
100
100
100
100
200
200
200
200
200
300
300
300
300
300
400
400
400
400
400
500
500
500
500
500

2. (A)
(B)
(C)
(D)
(E)

3. Solution (100 pts) E.

4. If then is
(A) (B)
(C) (D)
(E)

5. Solution (200 pts) A.

6. If then
(A) 8
(B) 2
(C) -2
(D) -3
(E) -8

7. Solution (300 pts) C. -2

8. If what is the value of at (3, 4)
(A) (B)
(C) (D)
(E)

9. Solution (400 pts) A.

10. Let f and g be differentiable functions with the following properties:
I for all x
II.
If and then
(B)
(C) (D) 0
(E) 2

11. Solution (500 pts) E. 2

12. (A) 1
(B)
(C)
(D)
(E) If
then

13. Solution (100 pts) E

14. The graph of the function
changes concavity at x =
(A) 3.29
(B) 2.21
(C) 1.34
(D) 0.41
(E)

15. Solution (200 pts) B

16. Let f be a function such that
For all x in the closed interval [3,4] with selected values shown in the table. Which of the following must be true about X
3.2
3.3
3.4
3.5
f(x)
2.48
2.68
2.86
3.03
(A)
(B)
(C)
(D)
(E)

17. Solution (300 pts) D

18. is concave down for
(A) (B)
(C)
(D)
(E)

19. Solution (400 pts) E

20. What are all the values of x for which the function f defined by
is increasing?
There are no such values of x
(B)
(C)
(D)
(E) All values of x

21. Solution (500 pts) D.

22. Let
For what value of x does
(A) -2
(B) -1
(C) 1
(D) 2
(E) 4

23. Solution (100 pts)
D 2

24. Let f be a function such that
Which of the following must be true?
f is continuous at x = 7
f is differentiable at x = 7
The derivative of f is continuous at x = 7
(A) I only
(B) II only
(C) I and II only
(D) I and III only
(E) II and III only

25. Solution (200 pts)
C I and II only

26. (A) 0
(B) 1
(C) 30
(D) 300
(E) 3000

27. Solution (300 pts)
D. 300

28. (A) 0
(B) 1/12
(C) 1/3
(D) 4/3
(E) nonexistent

29. Solution (400 pts)
B. 1/12

30. (A) -1 (B)
(C) (D)
(E)

31. Solution (500 pts) B.

32. An equation of the line tangent to the graph of at is
(A) (B)
(C) (D)
(E)

33. Solution (100 pts) C.

34. Let
then
(A) -1
(B) 0
(C) 1
(D) 2
(E) nonexistent

35. Solution (200 pts)
A. -1

36. The minimum acceleration attained on the interval 0 ≤ t ≤ 4
by the particle whose velocity is given by is
(A) -16
(B) -10
(C) -8
(D) -25/3
(E) -3

37. Solution (300 pts)
D. -25/3

38. The maximum value of on the interval [0, 2] is
(B) -7
(C) -2
(D) 0
(E) 2

39. Solution (400 pts)
D. 0

40. A particle is moving on the x-axis with position given by
Then the particle is at rest only when t =
(A) (B) and
(C) (D)
(E)

41. Solution (500 pts) E.

42. Which of the following is an equation of the line tangent to the graph of
at the point where
(A) (B)
(C) (D)
(E)

43. Solution (100 pts) A.

44. The side of a cube is increasing at a constant rate of 0
The side of a cube is increasing at a constant rate of 0.2 centimeter per second. In terms of the surface area S, what is the rate of change of the volume of the cube, in cubic centimeters per second?
(A) 0.1S
(B) 0.2S
(C) 0.6S
(D) 0.04S
(E) S

45. Solution (200 pts)
A. 0.1S

46. which of the following must be true?
Let f be a function that is differentiable on the open interval (-3, 7).
If f(-1) = 4, f(2) = -5 and f(6) = 8,
which of the following must be true?
I. f has at least 2 zeroes
II. f has a relative minimum at x = 2
III. For some c, 2 < c < 6, f(c) = 4
I only (B) II only
(C) I and II only (D) I and III only
(E) I, II, and III

47. Solution (300 pts)
D. I and III only

48. f(x) = 6 has a solution in (2, 5) f’(x) = 6 has a solution in (2, 5)
If f is continuous on [2, 5] and differentiable on (2, 5) with f(2) = -4 and f(5) = 14, which of the following statements must be true?
f(x) = 6 has a solution in (2, 5)
f’(x) = 6 has a solution in (2, 5)
f’’(x) = 6 has a solution in (2, 5)
(A) I only
(B) II only
(C) I and II only
I and III only
(E) I, II, and III

49. Solution (400 pts)
C. I and II only

50. At the moment that a rectangle is 8 feet long and 3 feet wide, its length is increasing at 0.5 feet/minute and its width is decreasing at 1.5 feet/minute. The area is
(A) decreasing at 10.5 square feet/minute
(B) increasing at 13.5 square feet/minute
(C) increasing at 8.5 square feet/minute
(D) decreasing at 0.5 square feet/minute
(E) decreasing at 0.75 square feet/minute

51. (A) decreasing at 10.5 square feet/minute
Solution (500 pts)
(A) decreasing at 10.5 square feet/minute