C)
D)
Solve the problem.
61)
Suppose the demand for a certain item is given by D(p) =-3p2+ 2p + 8, where p represents the
price of the item. Find D'(p), the rate of change of demand with respect to price.
A)
D'(p) =-6p+ 2
B)
D'(p) =-3p+ 2
C)
D'(p) =-3p2+ 2
D)
D'(p) =-6p2+ 2
62)
A cube 5 inches on an edge is given a protective coating 0.2 inches thick. About how much coating
should a production manager order for 1200 cubes?
A)
About 36,000 in.3
B)
About 30,000 in.3
C)
About 6000 in.2
D)
About 18,000 in.2
Describe the end behavior of the function.
63)
f(x) = 5x4+ 5x + 11
A)
lim
x
f(x) = ; lim
x 
f(x) =
B)
lim
x
f(x) =; lim
x 
f(x) =
C)
lim
x
f(x) = ; lim
x 
f(x) =
D)
lim
x
f(x) =; lim
x 
f(x) =
Provide an appropriate response.
64)
Find f'(x) if f(x) =.
A)
f'(x) = 1
B)
f'(x) =
C)
f'(x) =2
D)
f'(x) = 0
List the x–values in the graph at which the function is not differentiable.
65)
A)
x = – 2, x = 2
B)
x = 0
C)
x = 2
D)
x = – 2, x = 0, x = 2
Solve the problem.
66)
A company training program determines that, on average, a new employee can do P(x) pieces of
work per day after s days of on–the–job training, where P(x) =90 + 60x
x + 5 . Find lim
x
5P(x).
A)
105
B)
30
C)
42
D)
Does not exist
Provide an appropriate response.
67)
Let f and g be functions that satisfy f'(4) = 2 and g'(4) = – 3. Find h'(4) for h(x) = 3f(x) – g(x) + 2.
A)
2
B)
9
C)
5
D)
11
Solve the problem.
68)
If an object moves along a line so that it is at y = f(x) =8x2 at time x (in seconds), find the velocity
at
x = 1 (y is measured in feet).
A)
160 ft/s
B)
6 ft/sec
C)
16 ft / s
D)
8 ft / s
C
69)
One hour after x milligrams of a particular drug are given to a person, the change in body
temperature T (in degrees Fahrenheit) is given by T =x21 –x
8 , where 0
x 3. Approximate the
changes in body temperature produced by changing the drug dosage from 1 to 1.8 milligrams.
Round to the nearest hundredth when necessary.
A)
0.25°F
B)
1.3°F
C)
2.93°F
D)
1.63°F
B
Provide an appropriate response.
70)
Determine where the function H(x) =x2+ 7
x2+ x – 6 is continuous.
A)
(–3, 2) (2, )
B)
(–, –3)
C)
(–, –3) (–3, 2) (2, )
D)
(–, –3) (–3, 2)
C
23
B
71)
Solve the inequality and express the answer in interval notation: x2– 4x
x + 5 > 0.
A)
(–5, 0) (4, )
B)
(4, )
C)
(–5, 0)
D)
(–5, )
72)
The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginal average cost
function.
A)
C‘(x) = 70x + 41
B)
C‘(x) = 35 –12
x2
C)
C‘(x) = 70 –41
x
D)
C‘(x) = 35x + 41 +12
x
Use the definition f'(x) =lim
h
0
f(x +
h) – f(x)
h to find the derivative at x.
73)
f(x) = 4x + 6x3
A)
4 + 6x2
B)
4 + 18x2
C)
4x + 18x3
D)
4x + 18x2
Provide an appropriate response.
74)
Find f'(x) if f(x) = 6x–2+ 8x3+ 11x.
A)
f(x) = – 12x–1+ 24x2
B)
f'(x) = – 12x–3+ 24x2+ 11
C)
f'(x) = – 12x–1+ 24x2+ 11
D)
f'(x) = – 12x–3+ 24x2
24
75)
Use a sign chart to solve the inequality. Express answers in interval notation.
x2+ 6 < 2x
A)
(2 , )
B)
{2}
C)
(–, –2)
D)
76)
Let C(x) be the cost function and R(x) the revenue function. Compute the marginal cost, marginal
revenue, and the marginal profit functions.
C(x) =0.0004x3– 0.012x2+ 100x + 10,000
R(x) =350x
A)
C'(x) =0.0012x2– 0.024x + 100
R'(x) =350
P'(x) =0.0012x2– 0.024x – 250
B)
C'(x) =0.0012x2– 0.024x + 100
R'(x) =350
P'(x) =-0.0012x2+ 0.024x + 250
C)
C'(x) =0.0012x2+ 0.024x + 100
R'(x) =350
P'(x) =0.0012x2+ 0.024x + 250
77)
Find d
dv (6v0.7 –v5.8)
A)
4.2v–0.3 –5.8v4.7
B)
4.2v–0.3 –5.8v–4.7
C)
4.2v–0.3 –5.8v4.8
D)
4.2v–0.3 –5.8v–4.8
78)
Find dy
dx for y =1
3x3+x7
10 .
A)
1
9x2+7x6
10
B)
7x6
9x2+ 10
C)
–x–2+7
10 x7
D)
–x–4+7
10 x6
79)
Find the values of x where the tangent line is horizontal for f(x) = 3x3– 2x2– 9.
A)
x = 0, x = – 4
9
B)
x = 0, x =4
9
C)
x = 0, x = – 2
3
D)
x = 0, x =2
3
Find the limit, if it exists.
80)
Find: lim
x
3
x – 3
x2– 3x
A)
1
3
B)
–1
3
C)
0
D)
Does not exist
Find average rate of change for the function over the given interval.
81)
y = x2+ 4x between x =2 and x =4
A)
16
B)
8
C)
10
D)
5
Find the equation of the tangent line to the curve when x has the given value.
82)
Find the equation of the tangent line to the graph of the function at the given value of x.
f(x) =x2+ 5x at x = 4
A)
y =1
20 x +1
5
B)
y = – 4
25 x +8
5
C)
y = – 39x – 80
D)
y = 13x – 16
Find the limit.
83)
Determine the limit.
lim
x
5+
f(x), where f(x) =x2
(x – 5)3
A)
5
B)
–
C)
D)
–2
List the x–values in the graph at which the function is not differentiable.
84)
A)
x = – 1
B)
x = 1
C)
x = 2
D)
x = 0
Find
y for the given values of x1 and x2.
85)
y = 2x + 3; x = 18, x = 0.5
A)
0.1
B)
0.5
C)
5
D)
1
Find the limit, if it exists.
86)
Let f(x) =x2– 3x – 10
x + 2 . Find lim
x–2f(x).
A)
5
B)
–7
C)
–2
D)
Does not exist
Find the instantaneous rate of change for the function at the value given.
87)
Find the instantaneous rate of change for the function f(x) = 5x2+ x at x = – 4.
A)
–39
B)
–14
C)
–41
D)
6
The graph of y = f(x) is shown. Use the graph to answer the question.
88)
Is f continuous at x =-3?
A)
No
B)
Yes
Find average rate of change for the function over the given interval.
89)
Find the average rate of change of y with respect to x if x changes from 3 to 5 in the function
y =x2+ 3x.
A)
22
B)
9
C)
11
D)
4
90)
y =1x3+ 7x2– 8 between x =-8 and x =3
A)
154
3
B)
82
11
C)
14
D)
82
3
28
Solve the problem.
91)
Suppose that the value V of a certain product decreases, or depreciates, with time t, in months,
where
V(t) =27 –16t2
(t + 2) 2 .
Find lim
t
V(t).
A)
23
B)
11
C)
16
D)
27
Provide an appropriate response.
92)
Find the slope of the graph f(x) = – x2+ 3x at the point (1, 2).
A)
2
B)
–2
C)
–1
D)
1
93)
The total profit from selling x units of doorknobs is P(x) =(6x – 7)(9x – 8). Find the marginal average
profit function.
A)
P‘(x) = 54x – 56
B)
P‘(x) = 54 –56
x2
C)
P‘(x) = 54x –111
D)
P‘(x) = 54 –111
x2
Solve the problem.
94)
The electric power p (in W) as a function of the current i (in A) in a certain circuit is given by
p(i) =10i2+51i. Find the instantaneous rate of change of p with respect to i for i =0.8 A.
A)
56.8 W/A
B)
59 W/A
C)
67 W/A
D)
47.2 W/A
Find the limit, if it exists.
95)
Given lim
x
4f(x) = – 2 and lim
x
4 g(x) = 5, find lim
x
4
[g(x) – f(x)]
– 4 f(x) .
A)
–3
8
B)
–7
8
C)
7
8
D)
3
8
Solve the problem.
96)
The demand equation for a certain item is p = 14 –x
1,000 and the cost equation is C(x) = 7,000 + 4x.
Find the marginal profit at a production level of 3,000 and interpret the result.
A)
$16; at the 3,000 level of production, profit will increase by approximately $16 for each unit
increase in production.
B)
$4; at the 3,000 level of production, profit will increase by approximately $4 for each unit
increase in production.
C)
$14; at the 3,000 level of production, profit will increase by approximately $14 for each unit
increase in production.
D)
$7; at the 3,000 level of production, profit will increase by approximately $7 for each unit
increase in production.
Provide an appropriate response.
97)
Find f'(x) if f(x) = 9x7/5 – 5x2+ 10000.
A)
f'(x) =63
5x2/5 – 10x + 4000
B)
f'(x) =63
5x6/5 – 10x
C)
f'(x) =63
5x6/5 – 10x + 4000
D)
f'(x) =63
5x2/5 – 10x
30
The graph of y = f(x) is shown. Use the graph to answer the question.
98)
Is f continuous at x =0?
A)
Yes
B)
No
Use the definition f'(x) =lim
h
0
f(x +
h) – f(x)
h to find the derivative at x.
99)
f(x) =13x – 5
A)
8
B)
13x
C)
13
D)
–13
Find dy.
100)
y = x 5x + 2
100)
A)
15x – 4
2 5x + 2 dx
B)
15x – 4
5x + 2 dx
C)
15x + 4
5x + 2 dx
D)
15x + 4
2 5x + 2 dx
Provide an appropriate response.
101)
Find the vertical asymptote(s) of the graph of the given function.
f(x) =x2– 100
(x – 9)(x + 3)
101)
A)
x = – 9
B)
y = 9, y = – 3
C)
x = 9, x = – 3
D)
x = 10, x = – 10