29) If f is a differentiable function and f(0) = -3 and f(6) = 6, then which of the following must be true?
I. There exists a c in [0,6] where f(c) = 0.
II. There exists a c in [0,6] where f ' (c) = 0.
III. There exists a c in [0,6] where f ' (c) = 3/2.
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. ![](images/Calc_AB_Section2_322.gif)
II. ![](images/Calc_AB_Section2_323.gif)
III. ![](images/Calc_AB_Section2_324.gif)
a) I only
b) II 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 = 2cos(x) , y = 2sin(x), and the y-axis is
a) ![](images/Calc_AB_Section2_325.gif)
*b) ![](images/Calc_AB_Section2_326.gif)
c) ![](images/Calc_AB_Section2_327.gif)
d) ![](images/Calc_AB_Section2_328.gif)
e) ![](images/Calc_AB_Section2_329.gif)
32) Air is pumped into a spherical balloon at a rate of 8cm3 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?
![](images/image_33_5.gif)
a) f is increasing on [-5, 5].
*b) f has a point of inflection at x = 10.
c) f has a local maximum at x = 0.
d) f is concave down on [0, 10].
e) f has a local minimum at x = -5.
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 = 5.
II. The particle is slowing down on [0, 2].
III. The particle is speeding up on [2, 5].
*a) II only
b) I 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![](images/Calc_AB_Section2_363.gif)
for 0 < x < 1, is revolved about the y-axis. Which of the following integrals gives the volume generated?
a) ![](images/Calc_AB_Section2_364.gif)
b) ![](images/Calc_AB_Section2_365.gif)
*c) ![](images/Calc_AB_Section2_366.gif)
d) ![](images/Calc_AB_Section2_367.gif)
e) ![](images/Calc_AB_Section2_368.gif)
36) If
then
is
a) ![](images/Calc_AB_Section2_370.gif)
b) ![](images/Calc_AB_Section2_371.gif)
c) ![](images/Calc_AB_Section2_372.gif)
d) ![](images/Calc_AB_Section2_373.gif)
*e) ![](images/Calc_AB_Section2_374.gif)
37) The sum of two positive integers x and y is 90. Find the value of x that minimizes
a) ![](images/Calc_AB_Section2_376.gif)
b) ![](images/Calc_AB_Section2_377.gif)
c) ![](images/Calc_AB_Section2_378.gif)
d) ![](images/Calc_AB_Section2_379.gif)
*e) ![](images/Calc_AB_Section2_380.gif)
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) ![](images/Calc_AB_Section2_382.gif)
*b) ![](images/Calc_AB_Section2_383.gif)
c) ![](images/Calc_AB_Section2_384.gif)
d) ![](images/Calc_AB_Section2_385.gif)
e) ![](images/Calc_AB_Section2_386.gif)
39) The function f is defined as![](images/Calc_AB_Section2_387.gif)
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 [3, 7].
d) f has a local maximum at x = 3.
e) f is concave up for x > 7.
40) The base of a solid is the region bounded by ![](images/Calc_AB_Section2_388.gif)
the x-axis, and
the line x = 7
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) ![](images/Calc_AB_Section2_389.gif)
b) ![](images/Calc_AB_Section2_390.gif)
c) ![](images/Calc_AB_Section2_391.gif)
*d) ![](images/Calc_AB_Section2_392.gif)
e) ![](images/Calc_AB_Section2_393.gif)
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 2 hours. Roughly how many hours does it take for the population to reach 10000?
a) ![](images/Calc_AB_Section2_394.gif)
*b) ![](images/Calc_AB_Section2_395.gif)
c) ![](images/Calc_AB_Section2_396.gif)
d) ![](images/Calc_AB_Section2_397.gif)
e) ![](images/Calc_AB_Section2_398.gif)
42) Given that F'(x)= f(x), find![](images/Calc_AB_Section2_399.gif)
a) ![](images/Calc_AB_Section2_400.gif)
b) ![](images/Calc_AB_Section2_401.gif)
c) ![](images/Calc_AB_Section2_402.gif)
*d) ![](images/Calc_AB_Section2_403.gif)
e) ![](images/Calc_AB_Section2_404.gif)
43) The line normal to
at x = m is parallel to the y-axis. What is m?
a) ![](images/Calc_AB_Section2_406.gif)
b) ![](images/Calc_AB_Section2_407.gif)
c) ![](images/Calc_AB_Section2_408.gif)
d) ![](images/Calc_AB_Section2_409.gif)
*e) ![](images/Calc_AB_Section2_410.gif)
44) f and g are two differentiable functions such that
f(1) = g(1) = 4f'(1) = g'(1) = 7f'(4) = 4g'(4) = 7
If
, then h'(1) is
a) ![](images/Calc_AB_Section2_411.gif)
b) ![](images/Calc_AB_Section2_412.gif)
c) ![](images/Calc_AB_Section2_413.gif)
d) ![](images/Calc_AB_Section2_414.gif)
*e) ![](images/Calc_AB_Section2_415.gif)
45) If
and y(0) = 7, then yln(2) =
a) ![](images/Calc_AB_Section2_416.gif)
b) ![](images/Calc_AB_Section2_417.gif)
c) ![](images/Calc_AB_Section2_418.gif)
*d) ![](images/Calc_AB_Section2_419.gif)
e) ![](images/Calc_AB_Section2_420.gif)