AP Calculus name______p____

Test Review #2

Calculators are allowed. Allow 15 minutes for the FR and 45 minutes for the MC.

Let f be a function with f(1) = 4 such that for all points (x, y) on the graph of f the slope is given by . (From 1998 AP Test, Question #4)

  1. Find the slope of the graph f at the point where x = 1.
  1. Write an equation for the line tangent to the graph of f at x =1 and use it to approximate f(1.2).
  1. Find f(x) by solving the separable differential equation with the initial condition f(1) = 4.
  1. Use your solution from part (c) to find f(1.2).

1.

In the earth’s atmosphere the speed of sound is a function of the altitude. The figure above consisting of 3 line segments shows the speed of sound in m/sec. as a function of altitude, a in meters. The graph is not drawn to scale. What is the average speed of sound in m/sec. on the interval [0, 32,000]?

(A) 295(B) 303.9(C) 304.4(D) 306.8(E) 312.8

  1. Let f be a continuous function such that . What is the value of ?

(A)4

(B)8

(C)12

(D)16

(E)32

  1. If , then the average rate of change of f on the interval [0, 2] is

(A)4

(B)8

(C)12

(D)16

(E)24

4.

If the complete polynomial graph of is given above, then the graph of , the derivative of , will cross the x-axis in exactly how many points?

(A)0(B) 1(C) 2(D) 3(E) 4

5. At what point on the curve is the tangent line vertical?

(A)(0, 0) only(B) (-1, 0) only(C) only

(D) (-1, 0) and (0, 0)(E) The tangent line is never vertical.

  1. A company manufactures x calculators weekly that can be sold for dollars each. The cost of manufacturing x calculators is given by . The number of calculators the company should manufacture weekly in order to maximize its weekly profit is

(A)611

(B)652

(C)683

(D)749

(E)754

7.

If f is the continuous function shown in the figure above, then the area of the shaded region is

(A) (B) (C)

(D) (E)

  1. A missile rises vertically from a point on the ground 75,000 feet from a radar station. If the missile is rising at the rate of 16,500 feet per minute at the instant when it is 38,000 feet high, what is the rate of change, in radians per minute, of the missile’s angle of elevation from the radar station at this instant?

(A) 0.175

(B) 0.219

(C) 0.227

(D) 0.469

(E) 0.507

  1. If three equal subdivisions of [0, 3] are used, what is the Trapezoidal Rule approximation of ?

(A)3

(B)9

(C)9.5

(D)10

(E)19

  1. Let R be the region in the first quadrant enclosed by the lines x = 0 and y = 2 and the graph of . The volume of the solid generated when R is revolved about the x-axis is given by

(A) (B) (C)

(D) (E)

11.

b c

The figure above shows the graph of , the second derivative of a function . The function is continuous for all x. Which of the following statements about f are true?

  1. f is concave up for x < 0 and bxc.
  2. f has a relative minimum in the open interval bxc.
  3. f has points of inflection at x = 0 and x = b.

(A)I only

(B)II only

(C)III only

(D)I and III only

(E)I, II, and III only

12. Which statement is true for the function on the open interval ?

(A) is increasing at an increasing rate.

(B) is increasing at a decreasing rate.

(C) has an absolute maximum in the open interval.

(D) has a point of inflection in the open interval.

(E) has a point of symmetry in the open interval.

  1. If , which of the following must be true?

I.

II. is continuous at x = 2

III. has a horizontal tangent line at x = 2

(A)I only

(B)II only

(C)I and II only

(D)II and III only

(E)I, II, and III

  1. How many extrema (maximum and minimum) does the function have on the open interval -3 < x < 6?

(A)None

(B)One

(C)Two

(D)Three

(E)Four

  1. If , then a =

(A) 1.4

(B) 1.5

(C) 1.6

(D) 1.7

(E)1.8