29) If f is a differentiable function and f(0) = -6 and f(2) = 12, 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.

a) II and III only
b) I only
c) II only
d) I, II and III
*e) I and III only
30) Which of the following function(s) is continuous and differentiable?
I.
II.
III.
a) II only
b) I only
c) III 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 = 6cos(x) , y = 6sin(x), and the y-axis is
*a)
b)
c)
d)
e)
32) Air is pumped into a spherical balloon at a rate of 6cm3 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 point of inflection at x = 4.
b) f is increasing on [-2, 2].
c) f has a local maximum at x = 0.
d) f is concave down on [0, 4].
e) f has a local minimum at x = -2.
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 = 6.
II. The particle is slowing down on [0, 4].
III. The particle is speeding up on [4, 6].
a) II and III only
b) I only
*c) II 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 30. 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 6

Which of the following is false?
a) f is concave up for x > 6.
b) f is decreasing on [2, 6].
c) f has a local maximum at x = 2.
*d) f has a horizontal asymptote at y = 1.
e) f has a vertical asymptote at x = 6.
40) The base of a solid is the region bounded by

the x-axis, and

the line x = 3

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 3 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) = 5
f'(1) = g'(1) = 9
f'(5) = 5
g'(5) = 9

If , then h'(1) is
a)
b)
c)
*d)
e)
45) If and y(0) = 4, then yln(2) =
*a)
b)
c)
d)
e)