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Chapter
2
1. The derivative of 
is
is
A) 
B) 
C) 
D) 
B) C) D)
Ans: B Difficulty: moderate Section: 2.1
2. The derivative of 
is
is
A) 
B) 
C) 
D) 
B) C) D)
Ans: A Difficulty: moderate Section: 2.1
3. The derivative of 
is
is
A) 
B) 
C) 
D) 
B) C) D)
Ans: A Difficulty: moderate Section: 2.1
4. The derivative of 
is
is
A) 
B) 
C) 
D) 
B) C) D)
Ans: A Difficulty: moderate Section: 2.1
5. True or False: The derivative of 
is 2x + 5.
is 2x + 5.
Ans: False Difficulty: easy Section: 2.1
6. True or False: The derivative of is 2x + 5.
is 2x + 5.
Ans: False Difficulty: easy Section: 2.1
7. The equation of the line tangent to the graph
of 
at x = 2 is
at x = 2 is
A) y = 7x – 4 B) y
= 7x – 422 C) y = 7x – 2 D) y
= 7x – 144
Ans: A Difficulty: moderate Section: 2.1
8. The equation of the line tangent to the graph
of 
at x = 6 is
at x = 6 is
A) y =
20x – 36 B) y =
20x – 1728 C) y =
20x – 6 D) y =
20x – 216
Ans: A Difficulty: moderate Section: 2.1
9. True or False: The tangent to the graph of 
at x = 3 has
slope 
.
at x = 3 has
slope .
Ans: True Difficulty: moderate Section: 2.1
10. True or False: The tangent to the graph of 
at x = 3 has
slope of .
at x = 3 has
slope of .
Ans: True Difficulty: moderate Section: 2.1
11. The equation of the line tangent to the graph
of 
at x = 1 is
at x = 1 is
A) 
B) 
C) 
D) 
B) C) D)
Ans: C Difficulty: moderate Section: 2.1
12. True or False: The tangent to the graph of 
at x = 2 has
slope 
.
at x = 2 has
slope .
Ans: False Difficulty: moderate Section: 2.1
13. True or False: The tangent to the graph of 
at x = 2 has
slope of .
at x = 2 has
slope of .
Ans: False Difficulty: moderate Section: 2.1
14. For f(x) = 5 – x2,
find the slope of the secant line connecting the points whose x-coordinates
are x = –4 and x = –3.9.
Then use calculus to find the slope of the line that is tangent to the
graph of f at x = –4.
Ans: Slope of secant line: 7.9;
Slope of tangent line: 8
Difficulty: moderate Section: 2.1
15. For 
, find the average rate of change of f(x) with
respect to x as x changes from 144 to 145. Then use calculus to find the instantaneous
rate of change at x = 144.
, find the average rate of change of f(x) with
respect to x as x changes from 144 to 145. Then use calculus to find the instantaneous
rate of change at x = 144.
A) Average rate of change: 0.000864;
Instantaneous rate of change:
–0.125
B) Average rate of change: –0.000864;
Instantaneous rate of change:
0.000868
C) Average rate of change: –0.000864;
Instantaneous rate of change:
0.125
D) Average rate of change: 0.000864;
Instantaneous rate of change:
0.000868
Ans: D Difficulty: hard Section: 2.1
16. If f(x) represents the price per
barrel of oil in terms of time, what does 
represent? What about 
?
represent? What about ?
Ans: The average rate of change of oil price with
respect to time on the time interval [x0, x0
+ h]; the instantaneous rate of
change of oil price with respect to time at time x0.
Difficulty: easy Section: 2.1
17. A spherical balloon is being filled with air
in such a way that its radius is increasing at the constant rate of 2 cm/sec.
At what rate is the volume of the balloon increasing at the instant when its
surface has area 
? (Note: A sphere of
radius r has volume 
and surface area 
.)
? (Note: A sphere of
radius r has volume and surface area .)
Ans: 8p cm 
/sec
/sec
Difficulty: hard Section: 2.1
18. True or False: Differentiating 
gives 
.
gives .
Ans: False Difficulty: easy Section: 2.2
19. True or False: Differentiating 
gives 
.
gives .
Ans: False Difficulty: easy Section: 2.2
20. Differentiate 
A) 
B) 
C) 
D) 
B) C) D)
Ans: C Difficulty: easy Section: 2.2
21. Differentiate: 
A) B) 
C) 
D)
B) C) D)
Ans: A Difficulty: easy Section: 2.2
22. True or False: Differentiating 
gives 
.
gives .
Ans: True Difficulty: easy Section: 2.2
23. True or False: Differentiating 
gives 
.
gives .
Ans: True Difficulty: easy Section: 2.2
24. True or False: The equation of the line
tangent to the graph of that passes through
(1, 4) is y = 2x + 3.
that passes through
(1, 4) is y = 2x + 3.
Ans: False Difficulty: moderate Section: 2.2
25. True or False: The equation of the line
tangent to the graph of 
that passes through
(9, 9) is 2x + 6.
that passes through
(9, 9) is 2x + 6.
Ans: False Difficulty: moderate Section: 2.2
26. If 
, differentiate f(x).
, differentiate f(x).
Ans: 
Difficulty: moderate Section: 2.2
27. Differentiate 
A) 0
B) x C) 
D) 
D)
Ans: D Difficulty: easy Section: 2.2
28. Differentiate:
A) B) 0
C) 1 D)
B) 0
C) 1 D)
Ans: A Difficulty: easy Section: 2.2
29. Differentiate: 
.
.
Ans: 
Difficulty: moderate Section: 2.2
30. Differentiate 
.
.
Ans: 
Difficulty: easy Section: 2.2
31. Differentiate: 
.
.
Ans: 
Difficulty: easy Section: 2.2
32. Find the equation of the tangent line to the
curve 
at the point (1, 8)
at the point (1, 8)
Ans: y = x + 7.
Difficulty: moderate Section: 2.2
33. Find the equation of the tangent line to the
curve 
at the point (1, 1).
at the point (1, 1).
Ans: y = x
Difficulty: moderate Section: 2.2
34. Find the equation of the tangent to the graph
of 
at the point (1, 8).
at the point (1, 8).
Ans: y = –7x
+ 15
Difficulty: moderate Section: 2.2
35. Find the equation of the tangent to the graph
of 
at the point (1, 12).
at the point (1, 12).
Ans: y = 2x
+ 9
Difficulty: moderate Section: 2.2
36. Find the equation of the tangent line to the
graph of 
at (1, 2).
at (1, 2).
A) Not defined
B) y
= 2 C)
x = 1 D) y = 2x
Ans: D Difficulty: moderate Section: 2.2
37. Find the equation of the tangent line to the
graph of 
at the point (4, 20).
at the point (4, 20).
A) y = 8x
– 12 B) Not defined
C) y
= 20 D) x = 4
Ans: A Difficulty: moderate Section: 2.2
38. Find the equation of the line that is tangent
to the curve 
at the point (1, 7).
at the point (1, 7).
Ans: y = x + 6
Difficulty: moderate Section: 2.2
39. Find the equation of the line that is tangent
to the curve 
at the point (1, 17).
at the point (1, 17).
Ans: y = 16x + 1
Difficulty: moderate Section: 2.2
40. Find the equation of the tangent line to the
graph of 
at 
.
at .
A) 
B) 
C) y = –x + 1 D) 
B) C) y = –x + 1 D)
Ans: A Difficulty: moderate Section: 2.2
41. Find the equation of the tangent line to the
graph of at the point 
.
at the point .
A) 
B) 
C) 
D) 
B) C) D)
Ans: A Difficulty: moderate Section: 2.2
42. Find the equation of the tangent line to the
curve 
at the point where x
= 1.
at the point where x
= 1.
Ans: y = –5x
+ 8.
Difficulty: moderate Section: 2.2
43. Find the equation of the tangent line to the
curve at the point where x
= 1.
at the point where x
= 1.
Ans: y = –5x + 8
Difficulty: moderate Section: 2.2
44. The gross national product (GNP) of a certain
country is 
billion dollars where
t is the number of years after 1990. At what percentage rate will the
GNP be changing with respect to time in 1995?
billion dollars where
t is the number of years after 1990. At what percentage rate will the
GNP be changing with respect to time in 1995?
Ans: 8.07
Difficulty: hard Section: 2.2
45. True or False: An environmental study of a
certain suburban community suggests that t years from now the average
level of carbon monoxide in the air will be 
ppm. The rate that
the carbon monoxide level will change with respect to time 2 years from now
will be 0.048 ppm/yr.
ppm. The rate that
the carbon monoxide level will change with respect to time 2 years from now
will be 0.048 ppm/yr.
Ans: False Difficulty: hard Section: 2.2
46. True or False: The gross annual earnings of a
certain company were 
thousand dollars where
t is the number of years since its formation in 1990. The gross annual
earnings with respect to t in 1995 are growing at 13.75%.
thousand dollars where
t is the number of years since its formation in 1990. The gross annual
earnings with respect to t in 1995 are growing at 13.75%.
Ans: True Difficulty: hard Section: 2.2
47. True or False: An environmental study of a
certain suburban community suggests that t years from now the average
level of carbon monoxide in the air will be 
parts per million
(ppm). The rate that the carbon monoxide level will change with respect to time
4 years from now will be 0.4 ppm/yr.
parts per million
(ppm). The rate that the carbon monoxide level will change with respect to time
4 years from now will be 0.4 ppm/yr.
Ans: False Difficulty: hard Section: 2.2
48. An appliance store manager estimates that for x
television ads run per day, 
refrigerators will be
sold per month. Find 
and interpret what it
tells us about sales.
refrigerators will be
sold per month. Find and interpret what it
tells us about sales.
A) 
203.36; they'll
sell about 203 refrigerators if they run 4 ads per day.
203.36; they'll
sell about 203 refrigerators if they run 4 ads per day.
B) 4.52; they'll
sell about 5 refrigerators if they run 4 ads per day.
4.52; they'll
sell about 5 refrigerators if they run 4 ads per day.
C) 4.52; sales will
be increasing at about 5 refrigerators per month per ad when they're running 4
ads.
4.52; sales will
be increasing at about 5 refrigerators per month per ad when they're running 4
ads.
D) 203.36; the
cost of refrigerators will be rising by $203.36 if they're selling 4 per day.
203.36; the
cost of refrigerators will be rising by $203.36 if they're selling 4 per day.
Ans: C Difficulty: easy Section: 2.2
49. An efficiency study at a certain factory
indicates that an average worker who arrives on the job at 8:00 A.M. will have
produced 
units t hours
later. At what rate, in units/hour, is the worker's rate of production changing
with respect to time at 9:00 A.M.?
units t hours
later. At what rate, in units/hour, is the worker's rate of production changing
with respect to time at 9:00 A.M.?
Ans: 27 units/hour
Difficulty: hard Section: 2.2
50. Find all points (x, y) on the
graph of the function 
with the property
that the tangent to the graph at (x, y) passes through the point
(4, 0).
with the property
that the tangent to the graph at (x, y) passes through the point
(4, 0).
A) (0, 0) and (4, 80) B)
(4, 80) C) (0, 0) and (8, 320) D)
(8, 320)
Ans: C Difficulty: moderate Section: 2.2
51. If the position of an object moving along a
straight line is given by 
at time t,
find the object's velocity as a function of time.
at time t,
find the object's velocity as a function of time.
A) 
C) 
C)
B) 
D) 
D)
Ans: D Difficulty: moderate Section: 2.2
52. The displacement function of a moving object
is described by 
. What is the object's
acceleration?
. What is the object's
acceleration?
A) 2t + 5 B) 2t C) t
D) 2
Ans: D Difficulty: hard Section: 2.2
53. The displacement function of a moving object
is described by 
. What is the
acceleration of the object as a function of time?
. What is the
acceleration of the object as a function of time?
A) 2
B) 2t + 2 C) 2t D) t
Ans: A Difficulty: moderate Section: 2.2
54. The displacement function of a moving object
is described by 
. What is the velocity
of the object as a function of t?
. What is the velocity
of the object as a function of t?
A) 
B) 
C) 3
D) 2
B) C) 3
D) 2
Ans: B Difficulty: easy Section: 2.2
55. An object moves along a line in such a way that
its position at time t is 
. Find the velocity
and acceleration of the object at time t. When is the object stationary?
. Find the velocity
and acceleration of the object at time t. When is the object stationary?
A) 
; a(t)
= 6t – 54; t = 5
and 13
; a(t)
= 6t – 54; t = 5
and 13
B) ; a(t)
= 6t – 54; t = 9
; a(t)
= 6t – 54; t = 9
C) 
; a(t)
= 6t – 18; t = 5
; a(t)
= 6t – 18; t = 5
D) ; a(t)
= 6t – 54; t = 5
; a(t)
= 6t – 54; t = 5
Ans: A Difficulty: moderate Section: 2.2
56. The displacement function of a moving object
is described by 
. What is the velocity
of the object as a function of time?
. What is the velocity
of the object as a function of time?
A) B) C) 3
D) 2
B) C) 3
D) 2
Ans: A Difficulty: easy Section: 2.2
57. True or False: If the displacement of a moving
object is 
, the acceleration is
6t.
, the acceleration is
6t.
Ans: True Difficulty: easy Section: 2.2
58. True or False: If the displacement of a moving
object is 
, the acceleration is
36t.
, the acceleration is
36t.
Ans: True Difficulty: easy Section: 2.2
59. If an object moves in such a way that after t
seconds, the distance from its starting point is 
meters, find the
acceleration after 2 seconds in meters/s 
.
meters, find the
acceleration after 2 seconds in meters/s .
Ans: –18 meters/s2
Difficulty: hard Section: 2.2
60. Differentiate 
A) 2x + 1 B) 6x
+ 1 C)
D) 
D)
Ans: C Difficulty: moderate Section: 2.3
61. Differentiate: 
.
.
A) 
B) 2x + 1 C)
16x + 1 D)
B) 2x + 1 C)
16x + 1 D)
Ans: A Difficulty: moderate Section: 2.3
62. What is the rate of change of 
with respect to t
when t = 4?
with respect to t
when t = 4?
A) 
B) 
C) 8
D) 
B) C) 8
D)
Ans: A Difficulty: hard Section: 2.3
63. If 
, what is 
?
, what is ?
Ans: 
Difficulty: moderate Section: 2.3
64. Differentiate 
A) 
B) 
C) 2x
D) –x
B) C) 2x
D) –x
Ans: A Difficulty: moderate Section: 2.3
65. Differentiate: 
.
.
A) 
B) 
C) 2x
D) –x
B) C) 2x
D) –x
Ans: A Difficulty: moderate Section: 2.3
66. If 
, what is ?
, what is ?
Ans: 
Difficulty: hard Section: 2.3
67. True or False: The equation of the line that
is tangent to the curve 
at the point (0, –5)
is y = 5x – 5.
at the point (0, –5)
is y = 5x – 5.
Ans: True Difficulty: hard Section: 2.3
68. True or False: The equation of the tangent
line to the curve 
at the point (0, –4)
is y = 4x – 4.
at the point (0, –4)
is y = 4x – 4.
Ans: True Difficulty: hard Section: 2.3
69. If 
, what is ?
, what is ?
Ans: 
Difficulty: moderate Section: 2.3
70. Find the equation of the line that is tangent
to the curve 
at the point (1, –1).
at the point (1, –1).
Ans: y = –9x + 8
Difficulty: hard Section: 2.3
71. If 
, what is ?
, what is ?
Ans: 
Difficulty: hard Section: 2.3
72. Find the equation of the tangent line to the
curve 
at the point (1, 2).
at the point (1, 2).
Ans: y = 14x – 12
Difficulty: hard Section: 2.3
73. What is the rate of change of 
with respect to t
when t = 5?
with respect to t
when t = 5?
A) 
B) 
C) 10
D) 
B) C) 10
D)
Ans: A Difficulty: hard Section: 2.3
74. What is the rate of change of 
with respect to t
when t = 18?
with respect to t
when t = 18?
A) 
B) 
C) 21
D) –21
B) C) 21
D) –21
Ans: A Difficulty: hard Section: 2.3
75. Find the equation of the normal line to 
at the point with x-coordinate
–2.
at the point with x-coordinate
–2.
Ans: 
Difficulty: moderate Section: 2.3
76. Find an equation for the tangent line to the
curve 
at the point where x
= –1.
at the point where x
= –1.
Ans: 
Difficulty: hard Section: 2.3
77. Find 
, where 
.
, where .
Ans: 
Difficulty: hard Section: 2.3
78. Find , where 
.
, where .
Ans: 6x
Difficulty: easy Section: 2.3
79. The temperature in degrees Fahrenheit inside
an oven t minutes after turning it on can be modeled with the function
. Find 
and interpret what it
tells us about the temperature. Round
your answer to 2 decimal places.
Ans: 
; After 5
minutes, the temperature is increasing at the rate of 9.17 degrees per minute.
; After 5
minutes, the temperature is increasing at the rate of 9.17 degrees per minute.
Difficulty: easy Section: 2.3
80. It is estimated that t years from now,
the population of a certain suburban community will be 
thousand people. At
what rate will the population be growing 4 years from now?
thousand people. At
what rate will the population be growing 4 years from now?
Ans: 29 people/year
Difficulty: hard Section: 2.3
81. Find 
if 
.
if .
A) 
C) 
C)
B) 
D) 
D)
Ans: B Difficulty: moderate Section: 2.3
82. True or False: If 
, then 
.
, then .
Ans: True Difficulty: moderate Section: 2.3
83. Find 
if 
if
A) 
C) 
C)
B) 
D) 
D)
Ans: C Difficulty: moderate Section: 2.3
84. Find 
if 
and 
.
if and .
Ans: 
Difficulty: hard Section: 2.4
85. Find if 
and 
.
if and .
Ans: 
Difficulty: hard Section: 2.4
86. Find if 
and 
if and
Ans: 
Difficulty: hard Section: 2.4
87. Find if and 
if and
Ans: 
Difficulty: hard Section: 2.4
88. Find if 
and 
.
if and .
Ans: 
Difficulty: hard Section: 2.4
89. Find if 
and 
if and
Ans: 
Difficulty: hard Section: 2.4
90. True or False: If 
, then 
.
, then .
Ans: False Difficulty: moderate Section: 2.4
91. True or False: If 
, then 
.
, then .
Ans: False Difficulty: moderate Section: 2.4
92. True or False: An equation for the tangent
line to the curve 
at the point where x
= 1 is 
.
at the point where x
= 1 is .
Ans: False Difficulty: moderate Section: 2.4
93. An equation for the tangent line to the curve 
at the point where x
= 1 is:
at the point where x
= 1 is:
A) y = 9x – 8 B) y = 9x
C) y
= 2x + 1 D) y = 9x – 1
Ans: A Difficulty: moderate Section: 2.4
94. Find an equation for the tangent line to the
curve 
at the point where x
= 0.
at the point where x
= 0.
A) y =
14x + 1 B) y =
24x + 3 C) y = 3x
+ 1 D)
y = 3x – 1
Ans: D Difficulty: moderate Section: 2.4
95. An equation for the tangent line to the curve 
at the point where x
= 1 is
at the point where x
= 1 is
A) y =
24x – 23 B) y =
24x C) y = 5x
+ 1 D)
y = 24x – 1
Ans: A Difficulty: moderate Section: 2.4
96. An equation for the tangent line to the curve 
at the point where x
= 0 is
at the point where x
= 0 is
A) y = 5x
– 1 B)
y = 10x + 1 C) y = 5x + 1 D) y = 10x – 1
Ans: A Difficulty: moderate Section: 2.4
97. True or False: An equation for the tangent
line to the curve 
at the point where x
= –1 is y = 72x + 56.
at the point where x
= –1 is y = 72x + 56.
Ans: True Difficulty: moderate Section: 2.4
98. Find an equation for the tangent line to the
curve 
at the point where x
= –1.
at the point where x
= –1.
Ans: y = 0.11x + 1.42
Difficulty: hard Section: 2.4
99. Find all points on the graph of the function 
where the tangent line
is horizontal.
where the tangent line
is horizontal.
Ans: (0, 0) and (–3, –108)
Difficulty: moderate Section: 2.4
100. Find all points on the graph of the function 
where the tangent line
is horizontal.
where the tangent line
is horizontal.
A) There are none. B)
(2, 1) C) (0, 0) and (–4, –8) D)
(0, 0)
Ans: C Difficulty: moderate Section: 2.4
101. True or False: If 
, then 
at x = 0 and x = 2.
, then at x = 0 and x = 2.
Ans: False Difficulty: hard Section: 2.4
102. True or False: If 
, then 
.
, then .
Ans: False Difficulty: moderate Section: 2.4
103. If 
represents the height
in inches of a sapling y weeks after germination, find 
and interpret what it
tells us about the height of the tree.
Round your answer to 1 decimal place.
represents the height
in inches of a sapling y weeks after germination, find and interpret what it
tells us about the height of the tree.
Round your answer to 1 decimal place.
Ans: after 5 weeks, the tree is growing at 1.1
inches per week.
Difficulty: easy Section: 2.4
104. At a certain factory, the total cost of
manufacturing q units during the daily production run is 
dollars. It has been
determined that approximately 
units are
manufactured during the first t hours of a production run. Compute the
rate at which the total manufacturing cost is changing with respect to time 2
hours after production begins.
dollars. It has been
determined that approximately units are
manufactured during the first t hours of a production run. Compute the
rate at which the total manufacturing cost is changing with respect to time 2
hours after production begins.
Ans: It is increasing at $8,332.80/hour
Difficulty: hard Section: 2.4
105. When toasters are sold for p dollars
apiece, local consumers will buy 
toasters a month. It
is estimated that t months from now, the price of the toasters will be 
dollars. Compute the
rate at which the monthly demand for the toasters will be changing with respect
to time 16 months from now.
toasters a month. It
is estimated that t months from now, the price of the toasters will be dollars. Compute the
rate at which the monthly demand for the toasters will be changing with respect
to time 16 months from now.
Ans: Decreasing by 18 toasters/month
Difficulty: hard Section: 2.4
106. True or False: When a certain commodity is
sold for p dollars per unit, consumers will buy 
units per month. It
is estimated that t months from now, the price of the commodity will be 
dollars per unit. The
monthly demand will be decreasing 40 months from now.
units per month. It
is estimated that t months from now, the price of the commodity will be dollars per unit. The
monthly demand will be decreasing 40 months from now.
Ans: True Difficulty: hard Section: 2.4
107. When a certain commodity is sold for p
dollars per unit, consumers will buy 
units per month. It
is estimated that t months from now, the price of the commodity will be 
dollars per unit. The
approximate rate at which the monthly demand will be changing with respect to
time in 27 months is
units per month. It
is estimated that t months from now, the price of the commodity will be dollars per unit. The
approximate rate at which the monthly demand will be changing with respect to
time in 27 months is
A) –35 units per month C) –31.5
units per month
B) 35 units per month D) –131.5
units per month
Ans: A Difficulty: hard Section: 2.4
108. It is estimated that t years from now,
the population of a certain suburban community will be 
thousand people. At
what rate, in people/year will the population be growing 3 years from now?
thousand people. At
what rate, in people/year will the population be growing 3 years from now?
Ans: 285.7 people/year
Difficulty: hard Section: 2.4
109. True or False: It is estimated that t
years from now, the population of a certain suburban community will be 
thousand. An environmental
study indicates that the average daily level of carbon monoxide in the air will
be 
parts per million
(ppm) when the population is p thousand. The rate at which the level of
pollution is changing with respect to time 3 years from now is about 0.084 ppm
per year.
thousand. An environmental
study indicates that the average daily level of carbon monoxide in the air will
be parts per million
(ppm) when the population is p thousand. The rate at which the level of
pollution is changing with respect to time 3 years from now is about 0.084 ppm
per year.
Ans: True Difficulty: hard Section: 2.4
110. It is estimated that t years from now,
the population of a certain community will be 
thousand. An
environmental study indicates that the average daily level of carbon monoxide
in the air will be 
units when the
population is p thousand. The rate at which the level of carbon monoxide
will be changing 3 years from now is
thousand. An
environmental study indicates that the average daily level of carbon monoxide
in the air will be units when the
population is p thousand. The rate at which the level of carbon monoxide
will be changing 3 years from now is
A) –0.078 ppm per thousand people C) 1.000
ppm per thousand people
B) 0.078 ppm per thousand people D) –1.000
ppm per thousand people
Ans: B Difficulty: hard Section: 2.4
111. True or False: The function 
will decrease by
approximately 0.6 as x decreases from 3 to 2.7.
will decrease by
approximately 0.6 as x decreases from 3 to 2.7.
Ans: False Difficulty: hard Section: 2.5
112. The largest percentage error you can allow in
the measurement of the radius of a sphere if you want the error in the
calculation of its surface area using the formula to be no greater than
6 percent is about:
to be no greater than
6 percent is about:
A) 6%
B) 3% C)
1% D) 2%
Ans: B Difficulty: hard Section: 2.5
113. You measure the side of a cube to be 11
centimeters long and conclude that the volume of the cube is 
cubic centimeters. If
your measurement of the side is accurate to within 2% , approximately how
accurate is your calculation of this volume?
cubic centimeters. If
your measurement of the side is accurate to within 2% , approximately how
accurate is your calculation of this volume?
A) Maximum error in volume is about
± 7.26 cm
B) Maximum error in volume is about
± 79.86 cm
C) Maximum error in volume is about
± 0.66 cm
D) Maximum error in volume is about
± 878.46 cm
Ans: B Difficulty: moderate Section: 2.5
114. If the total cost of manufacturing q
units of a certain commodity is C(q) = (3q + 1)(5q
+ 7), use marginal analysis to estimate the cost of producing the 19th unit, in
dollars.
Ans: 596 dollars
Difficulty: hard Section: 2.5
115. An efficiency study of the morning shift at a
certain factory indicates that an average worker arriving on the job at 8:00
A.M. will have assembled 
transistor radios x
hours later. Approximately how many radios will the worker assemble between
11:00 and 11:45 A.M.?
transistor radios x
hours later. Approximately how many radios will the worker assemble between
11:00 and 11:45 A.M.?
A) Approximately 19 radios C) Approximately 14 radios
B) Approximately 855 radios D) Approximately 39 radios
Ans: C Difficulty: moderate Section: 2.5
116. True or False: If 
, then 
.
, then .
Ans: False Difficulty: moderate Section: 2.6
117. Find , where 
.
, where .
A) 
B) 
C) 
D) 
B) C) D)
Ans: B Difficulty: moderate Section: 2.6
118. Find , where 
.
, where .
Ans: 
Difficulty: moderate Section: 2.6
119. Find , where 
.
, where .
Ans: 
Difficulty: moderate Section: 2.6
120. True or False: If 
, then 
.
, then .
Ans: False Difficulty: moderate Section: 2.6
121. True or False: If 
, then 
.
, then .
Ans: False Difficulty: moderate Section: 2.6
122. True or False: If 
, then 
.
, then .
Ans: False Difficulty: moderate Section: 2.6
123. Find an equation for the tangent line to the
curve 
at the point (1, 0).
at the point (1, 0).
Ans: y = –2x + 2
Difficulty: hard Section: 2.6
124. Find the slope of the tangent line to the
curve 
at the point (1, 1).
at the point (1, 1).
A) 5
B) 1 C)
–5 D) 3
Ans: C Difficulty: hard Section: 2.6
125. Find an equation for the tangent line to the
curve 
at the point (1, –1).
at the point (1, –1).
Ans: 
Difficulty: hard Section: 2.6
126. Find the equation of the tangent line to the
given curve at the specified point: 
; (0, 11)
; (0, 11)
A) 
B) 
C) y = –47x + 11 D) y
= 47x + 11
B) C) y = –47x + 11 D) y
= 47x + 11
Ans: C Difficulty: moderate Section: 2.6
127. True or False: The equation for the tangent
line to the curve 
at the point (1, –1)
is y = –1.
at the point (1, –1)
is y = –1.
Ans: True Difficulty: hard Section: 2.6
128. Use implicit differentiation to find 
for 
.
for .
A) 
B) 
C) 
D) 
B) C) D)
Ans: B Difficulty: easy Section: 2.6
129. Find , where 
.
, where .
Ans: 
Difficulty: moderate Section: 2.6
130. In a certain factory, output Q is
related to inputs x and y by the equation 
. If the current
levels of input are x = 255 and y = 155, use calculus to estimate
the change in input y that should be made to offset a decrease of 0.6
unit in input x so that output will be maintained at its current level.
. If the current
levels of input are x = 255 and y = 155, use calculus to estimate
the change in input y that should be made to offset a decrease of 0.6
unit in input x so that output will be maintained at its current level.
A) An increase of 0.37 C) It
cannot be determined
B) A decrease of 0.37 D) No
change
Ans: A Difficulty: moderate Section: 2.6
131. The output at a certain plant is 
units per day, where x
is the number of hours of skilled labor used and y is the number of
hours of unskilled labor used. Currently 60 hours of skilled labor and 150
hours of unskilled labor are used each day. Use calculus to estimate the change
in unskilled labor that should be made to offset a 1 hour increase in skilled
labor so that output will remain the same.
units per day, where x
is the number of hours of skilled labor used and y is the number of
hours of unskilled labor used. Currently 60 hours of skilled labor and 150
hours of unskilled labor are used each day. Use calculus to estimate the change
in unskilled labor that should be made to offset a 1 hour increase in skilled
labor so that output will remain the same.
A) An increase of 1.24 hours C) It cannot be determined
B) A decrease of 1.24 hours D) No change
Ans: B Difficulty: hard Section: 2.6
132. Suppose the output at a certain factory is 
units, where x
is the number of hours of skilled labor used and y is the number of
hours of unskilled labor. The current labor force consists of 30 hours of
skilled labor and 30 hours of unskilled labor. Use calculus to estimate the
change in unskilled labor y that should be made to offset a 1-hour
increase in skilled labor x so that output will be maintained at its
current level.
units, where x
is the number of hours of skilled labor used and y is the number of
hours of unskilled labor. The current labor force consists of 30 hours of
skilled labor and 30 hours of unskilled labor. Use calculus to estimate the
change in unskilled labor y that should be made to offset a 1-hour
increase in skilled labor x so that output will be maintained at its
current level.
A) –2.55 hours
B) –1.76 hours C)
–0.39 hours D) 0.39 hours
Ans: A Difficulty: moderate Section: 2.6
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