29) If f is a differentiable function and f(0) = -4 and f(5) = 8, then which of the following must be true?
I. There exists a c in [0,5] where f(c) = 0.
II. There exists a c in [0,5] where f ' (c) = 0.
III. There exists a c in [0,5] where f ' (c) = 12/5.

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) I and III only
b) III only
c) I and II only
d) I only
e) II only
31) The area of the region in the first quadrant bounded by the graphs of y = 7cos(x) , y = 7sin(x), and the y-axis is
a)
b)
c)
d)
e)
32) Air is pumped into a spherical balloon at a rate of 7cm3 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 is concave down on [0, 12].
b) f is increasing on [-6, 6].
c) f has a local maximum at x = 0.
d) f has a local minimum at x = -6.
e) f has a point of inflection at x = 12.
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 = 2 and x = 6.
II. The particle is slowing down on [0, 2].
III. The particle is speeding up on [2, 6].
a) I, II and III
b) II and III only
c) I and III only
d) II only
e) I only
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 150. 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 is concave up for x > 7.
b) f is decreasing on [4, 7].
c) f has a local maximum at x = 4.
d) f has a horizontal asymptote at y = 1.
e) f has a vertical asymptote at x = 7.
40) The base of a solid is the region bounded by

the x-axis, and

the line x = 2

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 6 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) = 3
f'(1) = g'(1) = 6
f'(3) = 3
g'(3) = 6

If , then h'(1) is
a)
b)
c)
d)
e)
45) If and y(0) = 3, then yln(2) =
a)
b)
c)
d)
e)