AP CALCULUS Review for Test 3 NAME

AP CALCULUS Review for Test 3 NAME:

No Calculator Except Problems 14, 27

1. Find all intervals on which is decreasing.

a. b. c. and

d. , (-2,1) and e. None of these

1. Find all critical numbers: .

a. 0b. 3c. –3, 3

d. –3, 0, 3e. None of these

1. Find the values of x that give relative extrema for the function .

1. Relative maximum: x = -1; Relative minimum: x =1.

1. Relative maximum: x = 1, x = 3; Relative minimum: x = -1.

1. Relative minimum: x = 2

1. Relative maximum: x = -1; Relative minimum: x = 2

1. None of these

1. Find all intervals on which the function is concave upward: .

a. b. c.

d. e. None of these

1. Let and let have critical numbers –2, 0, 2. Find the x coordinate of any relative maximum of the function.

a. –2b. 2c. 0

d. –2 and 2e. None of these

1. Find

a. 4b. 0c. 2

d. e. None of these

1. Which of the following functions has a horizontal asymptote at ?

a. b. c.

d. e. None of these

1. Which of the following is the correct sketch of the graph of the function?

1. A farmer has 160 ft. of fencing to enclose 2 adjacent rectangular pigpens. What are the dimensions of the overall enclosed area such that the area will be a maximum?

a. ft by ftb. 40 ft by ftc. 20 ft by ft

d. 40 ft by 40 fte. None of these

1. Find all points of inflection: .

a. (0, 0), b. (0, 0)c. (2, 0), (-2, 0)

d. , e. None of these

1. Which of the following is the correct sketch of the graph of the function

1. The second derivative test is used to find points of inflection

a. nob. yesc. the square root of pi.

d. can’t telle. None of these

13. Find all absolute extrema in the interval if .

a. b. , (0, 0)c. , (0, -1)

d. , e. None of these.

1. The radius of a sphere is measured to be 3 inches. If the measurement is correct to within 0.01 inch, use differentials to estimate the propagated error in the volume of the sphere. Calculator OK

a. b. c.

d. e. None of these

FREE RESPONSE: SHOW ALL WORK

1. Investigate for intervals where is increasing or decreasing. (Key word is “investigate” which means applying Calculus to show evidence).

1. Find all critical numbers:.

1. Find extrema:

1. Find all relative extrema in the interval if

1. Find all intervals for which the function is concave downward.

1. Let . Use the Second Derivative Test to determine any relative extrema.

1. Find

1. Use the techniques learned in this class to sketch the graph of. Show all work (6pts).

1. Find all points of inflection:.

1. The management of a large box store plans to use 1,800 ft. of fencing to fence in a rectangular storage yard using the building as one side of the yard. If the fencing is used for the remaining 3 sides, find the area of the largest possible yard.

1. Find the limit:

1. Find all horizontal asymptotes:

1. a) The volume of a cube is claimed to be 27 cu.in., correct to within 0.027. Use differentials to estimate the propagated error in the measurement of the side of the cube. Calculator OK

b) The radius of a sphere is claimed to be 8 inches, correct to within 0.02 inches. Use differentials to estimate the propagated error in the volume of the sphere. Calculator OK

28. On the function f(x) above, a) Where is increasing? b) Where is positive?

c) Where is negative?

29. Examine the graph of f ‘ (x) below and describe and justify where f(x):

a) Is concave up? b) Has inflection point(s)

c) Has relative extrema d) is increasing?

30. a) sketch a function where f (x) is negative but f ‘(x) is increasing

b) sketch a function where f ‘’(x) is positive but f ‘(x) is negative with f(x) being positive

31. 32.

33. 34.

35. 36.

37. Use a light crayon to show everywhere the function is increasing and a darker crayon to show everywhere the function is decreasing. Estimate the x coordinates for all relative extrema and inflection points. Justify your answers.