29) If f is a differentiable function and f(0) = -3 and f(2) = 6, then which of the following must be true?
I. There exists a c in [0,2] where f(c) = 0.
II. There exists a c in [0,2] where f ' (c) = 0.
III. There exists a c in [0,2] where f ' (c) = 9/2.

a) II only
b) I only
c) I and III only
d) II and III only
e) I, II and III
30) Which of the following function(s) is continuous and differentiable?
I.
II.
III.
a) III only
b) II only
c) I only
d) I and II only
e) I and III only
31) The area of the region in the first quadrant bounded by the graphs of y = 4cos(x) , y = 4sin(x), and the y-axis is
a)
b)
c)
d)
e)
32) Air is pumped into a spherical balloon at a rate of 10cm3 per second. At what rate is the radius of the sphere changing when its volume is cm3?
a) cm/sec
b) cm/sec
c) cm/sec
d) cm/sec
e) cm/sec
33) The graph of the derivative of f is shown below. Which of the following must be true?

a) f has a local maximum at x = 0.
b) f is increasing on [-3, 3].
c) f has a point of inflection at x = 6.
d) f is concave down on [0, 6].
e) f has a local minimum at x = -3.
34) A particle is moving along the x-axis and its position at time t > 0 is given by
Which of the following is (are) true?
I. The particle changes direction at x = 4 and x = 5.
II. The particle is slowing down on [0, 4].
III. The particle is speeding up on [4, 5].
a) I only
b) II only
c) II and III only
d) I and III only
e) I, II and III
35) The region enclosed by the graphs of
and the line

for 0 < x < 1, is revolved about the y-axis. Which of the following integrals gives the volume generated?
a)
b)
c)
d)
e)
36) If
then is
a)
b)
c)
d)
e)
37) The sum of two positive integers x and y is 120. Find the value of x that minimizes
a)
b)
c)
d)
e)
38) A particle moves along a straight line, and its velocity at time t is given by
What is the total distance the particle travels from t = 1 to t = e?
a)
b)
c)
d)
e)
39) The function f is defined as

x 7

Which of the following is false?
a) f has a horizontal asymptote at y = 1.
b) f has a vertical asymptote at x = 7.
c) f is decreasing on [2, 7].
d) f has a local maximum at x = 2.
e) f is concave up for x > 7.
40) The base of a solid is the region bounded by

the x-axis, and

the line x = 8

Each cross-section of the solid perpendicular to the x-axis is a square, with one side on the xy-plane. Which of the following expressions represents the volume of the solid?
a)
b)
c)
d)
e)
41) The rate at which a bacteria population grows is proportional to the number of bacteria present. Initially, there were 1000 bacteria present and the population doubled in 5 hours. Roughly how many hours does it take for the population to reach 10000?
a)
b)
c)
d)
e)
42) Given that F'(x)= f(x), find

a)
b)
c)
d)
e)
43) The line normal to
at x = m is parallel to the y-axis. What is m?
a)
b)
c)
d)
e)
44) f and g are two differentiable functions such that
f(1) = g(1) = 4
f'(1) = g'(1) = 8
f'(4) = 4
g'(4) = 8

If , then h'(1) is
a)
b)
c)
d)
e)
45) If and y(0) = 5, then yln(2) =
a)
b)
c)
d)
e)