Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Use or where appropriate to describe the behavior at each zero of the denominator and identify all vertical
asymptotes.
1)
g(x) =x
6 – x
1)
A)
lim
x
6–f(x) =; lim
x
6+f(x) = ; x = 6 is a vertical asymptote
B)
lim
x
6–f(x) = ; lim
x
6+f(x) = ; x = 6 is a vertical asymptote
C)
lim
x
6–f(x) = ; lim
x
6+f(x) =; x = 6 is a vertical asymptote
D)
lim
x
6–f(x) =; lim
x
6+f(x) = ; x = 0 is a vertical asymptote
2)
f(0) =4 and lim
x
0 f(x) =4
2)
A)
B)
1
C)
D)
3)
f(–1) = –7 ; lim
x
(-1)–f(x) = –2; lim
x
(-1)+f(x) = –7
3)
A)
B)
2
C)
D)
Use the definition f'(x) =lim
h
0f(x + h) – f(x)
h to find the derivative at x.
4)
f(x) =9x – 16
4)
A)
9x
B)
9
C)
-7
D)
–9
Provide an appropriate response.
5)
Use the four step process to find f'(x) for the function f(x) =5x2– 3x.
5)
A)
10x + 5h – 3
B)
5h – 3
C)
10x – 3
D)
5h2– 3h
6)
Use the four step process to find f'(x) for the function f(x) =x
6 – x.
6)
A)
6
(x – 6)(x + h – 6)
B)
–x
(x – 6)(x + h – 6)
C)
1
(x – 6)(x + h – 6)
D)
–6
h(x – 6)(x + h – 6)
Solve the problem.
7)
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).
7)
A)
6 ft/sec
B)
160 ft/s
C)
8 ft / s
D)
16 ft / s
Find the instantaneous rate of change for the function at the value given.
8)
Find the instantaneous rate of change for the function x2+4x at x =6.
8)
A)
12
B)
10
C)
60
D)
16
Solve the problem.
9)
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).
9)
A)
42
B)
105
C)
30
D)
Does not exist
10)
V =4
3r3, where r is the radius, in centimeters. By approximately how much does the volume of a
sphere increase when the radius is increased from 1.0 cm to 1.1 cm? (Use 3.14 for .)
10)
A)
0.1 cm3
B)
1.3 cm3
C)
1.5 cm3
D)
1.1 cm3
Provide an appropriate response.
11)
Find the equation of the tangent line at x = – 6 for f(x) =x3
2. Write the answer in the form y = mx +
b.
11)
A)
y = 54x + 216
B)
y = 216x + 18
C)
y = 216x + 54
D)
y = 18x + 216
Use or where appropriate to describe the behavior at each zero of the denominator and identify all vertical
asymptotes.
12)
f(x) =x2– 16
x2+ 16
12)
A)
lim
x
4–f(x) =; lim
x
4+f(x) = ; x = 4 is a vertical asymptote
B)
lim
x
4–f(x) =; lim
x
4+f(x) =; x = 0 is a vertical asymptote
C)
lim
x –4–f(x) =; lim
x –4+f(x) = ; x = –4 is a vertical asymptote
D)
No zeros of denominator; no vertical asymptotes
Provide an appropriate response.
13)
Find the vertical asymptote(s) of the graph of the given function.
f(x) =x2– 100
(x – 9)(x + 3)
13)
A)
x = –9
B)
y = 9, y = –3
C)
x = 9, x = –3
D)
x = 10, x = –10
14)
The total cost in dollars of producing x lawn mowers is given by C(x) = 4,000 + 90x –x2
3. Find the
marginal average cost at x = 20, C‘(20) and interpret the result.
14)
A)
–$10.33; a unit increase in production will decrease the average cost per unit by
approximately $10.33 at a production level of 20 units.
B)
–$20.33; a unit increase in production will decrease the average cost per unit by
approximately $20.33 at a production level of 20 units.
C)
–$1.33; a unit increase in production will decrease the average cost per unit by approximately
$1.33 at a production level of 20 units.
D)
–$13.33; a unit increase in production will decrease the average cost per unit by
approximately $13.33 at a production level of 20 units.
15)
A spherical balloon is being inflated. Find the approximate change in volume if the radius
increases from 6.2 cm to 6.4 cm. (Recall that V =4
3r3.)
15)
A)
317.77 cm3
B)
30.752 cm3
C)
153.76 cm3
D)
0.992 cm3
Solve the problem.
16)
The cost of manufacturing a particular videotape is C(x) = 9000 + 9x, where x is the number of
tapes produced. The average cost per tape, denoted by C(x), is found by dividing C(x) by x. Find
lim
x
9000 C(x).
16)
A)
14
B)
10
C)
6
D)
Does not exist
6
Find the limit, if it exists.
17)
Let f(x) =
x2– 16
x + 4 if x > 0
x2– 16
x – 4 if x < 0
Find lim
x
0f(x).
17)
A)
0
B)
–4
C)
–
D)
Does not exist
18)
Let f(x) =
x2– 16
x + 4 if x > 0
x2– 16
x – 4 if x < 0
Find lim
x
0f(x).
18)
A)
B)
4
C)
–4
D)
Does not exist
Solve the problem.
19)
Suppose that the cost C of removing p% of the pollutants from a chemical dumping site is given by
C(p) =$40,000
100 – p .
Can a company afford to remove 100% of the pollutants? Explain.
19)
A)
No, the cost of removing p% of the pollutants increases without bound as p approaches 100.
B)
Yes, the cost of removing p% of the pollutants is $400, which is certainly affordable.
C)
No, the cost of removing p% of the pollutants is $400, which is a prohibitive amount of
money.
D)
Yes, the cost of removing p% of the pollutants is $40,000, which is certainly affordable.
Provide an appropriate response.
20)
Given f(x + h) – f(x) = 4xh + 4h + 2h2, find the slope of the tangent line at x = 4.
20)
A)
16
B)
20
C)
22
D)
8
21)
Find the slope of the graph f(x) = –x2+ 3x at the point (1, 2).
21)
A)
–1
B)
2
C)
1
D)
–2
22)
Find the derivative of y =3x5–7x2– 4
x2.
22)
A)
y=9x–2+8x–3
B)
y=18x2+8x–3
C)
y=9x2+8x–3
D)
y=9x2+8x3
Find the limit, if it exists.
23)
Evaluate the following limit
lim
x
2
1
x – 2
23)
A)
B)
–
C)
2
D)
Does not exist
24)
Find: lim
x
3
x2– 9
x – 3 +x2+ 7
24)
A)
3
B)
2
C)
10
D)
Does not exist
List the x–values in the graph at which the function is not differentiable.
25)
25)
A)
x = –2, x = 0, x = 2
B)
x = –2, x = 2
C)
x = 2
D)
x = 0
Provide an appropriate response.
26)
Determine the points at which the function is discontinuous.
h(x) =x2– 4 for x <-1
0 for -1 x 1
x2+ 4 for x >1
26)
A)
1
B)
–1, 0, 1
C)
–1, 1
D)
None
27)
Find f'(x) if f(x) = 6x–2+ 8x3+ 11x.
27)
A)
f'(x) = –12x–3+ 24x2+ 11
B)
f'(x) = –12x–3+ 24x2
C)
f'(x) = –12x–1+ 24x2+ 11
D)
f(x) = –12x–1+ 24x2
Find the equation of the tangent line to the curve when x has the given value.
28)
f(x) =-4–x2; x =4
28)
A)
y =-8x +12
B)
y = –2x
C)
y =8x –12
D)
y =4x +12
Find the limit, if it exists.
29)
Find: lim
x
3
x – 3
x2– 3x
29)
A)
–1
3
B)
1
3
C)
0
D)
Does not exist
Solve the problem.
30)
Suppose the demand for a certain item is given by D(p) =-3p2+ 4p + 8, where p represents the
price of the item. Find D'(p), the rate of change of demand with respect to price.
30)
A)
D'(p) =-6p+ 4
B)
D'(p) =-3p+ 4
C)
D'(p) =-3p2+ 4
D)
D'(p) =-6p2+ 4
Provide an appropriate response.
31)
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.
31)
A)
11
B)
5
C)
2
D)
9
Solve the problem.
32)
Suppose an object moves along the y–axis so that its location is y = f(x) =x2+ x at time x (y is in
meters and x is in seconds). Find the instantaneous velocity at x = 4 seconds.
32)
A)
20 m/s
B)
9 m/s
C)
10 m/s
D)
8 m/s
Provide an appropriate response.
33)
Find y’ if y = 6x.
33)
A)
0
B)
x2
C)
6
D)
x
Solve the problem.
34)
A pen manufacturer determined that the total cost in dollars of producing x dozen pens in one day
is given by:
C(x) = 350 + 2x – 0.01x2, 0 x 100
Find the marginal cost at a production level of 70 dozen pens and interpret the result.
34)
A)
The marginal cost is $0.62/doz. The cost of producing 1 dozen more pens at a production level
of 70 dozen pens is approximately $0.62.
B)
The marginal cost is $0.59/doz. The cost of producing 1 dozen more pens at a production level
of 70 dozen pens is approximately $0.59.
C)
The marginal cost is $0.58/doz. The cost of producing 1 dozen more pens at a production level
of 70 dozen pens is approximately $0.58.
D)
The marginal cost is $0.60/doz. The cost of producing 1 dozen more pens at a production level
of 70 dozen pens is approximately $0.60.
35)
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.
35)
A)
$14; at the 3,000 level of production, profit will increase by approximately $14 for each unit
increase in production.
B)
$7; at the 3,000 level of production, profit will increase by approximately $7 for each unit
increase in production.
C)
$16; at the 3,000 level of production, profit will increase by approximately $16 for each unit
increase in production.
D)
$4; at the 3,000 level of production, profit will increase by approximately $4 for each unit
increase in production.
36)
An object moves along the y–axis (marked in feet) so that its position at time t (in seconds) is given
by f(t) = 9t3– 9t2+ t + 7. Find the velocity at three seconds.
36)
A)
190 feet per second
B)
192 feet per second
C)
197 feet per second
D)
109 feet per second
37)
f(0) = 6; lim
x
0–f(x) = 0; lim
x
0+f(x) = 0
37)
A)
B)
C)
D)
Provide an appropriate response.
38)
Use a graphing utility to find the discontinuities of the given rational function.
f(x) =x2+ 2x + 1
x3+ 2x2+ 5x – 8
38)
A)
–1
B)
1
C)
3
D)
Continuous at all values of x
39)
Evaluate dy and
y for y = f(x) = 20 + 15x2–x3, x = 2, and dx =
x = 0.3.
39)
A)
dy = 14.4;
y = 15.183
B)
dy = 15.183;
y = 15.183
C)
dy = 15.183;
y = 14.4
D)
dy = 14.4;
y = 14.4
A
Find the limit, if it exists.
40)
Let f(x) =
x2– 16
x + 4 if x > 0
x2– 16
x – 4 if x < 0
Find lim
x
0f(x)
40)
A)
–4
B)
0
C)
4
D)
Does not exist
A
Solve the problem.
41)
Suppose an object moves along the y–axis so that its location is y = f(x) =x2+ x at time x (y is in
meters and x is in seconds). Find the average velocity for x changing from 3 to 3 + h seconds.
41)
A)
7 – h m/s
B)
7 + h m/s
C)
12 – h m/s
D)
12 + h m/s
B
13
B
List the x–values in the graph at which the function is not differentiable.
42)
42)
A)
x = –3, x = 3
B)
x = –3, x = 0, x = 3
C)
x = –2, x = 2
D)
x = –2, x = 0, x = 2
Provide an appropriate response.
43)
Find d
dv (6v0.7 –v5.8)
43)
A)
4.2v–0.3 –5.8v–4.7
B)
4.2v–0.3 –5.8v–4.8
C)
4.2v–0.3 –5.8v4.8
D)
4.2v–0.3 –5.8v4.7
Sketch a possible graph of a function that satisfies the given conditions.
44)
f(1) = 4; lim
x
1–f(x) = 4; lim
x
1+f(x) = 3
44)
14
A)
B)
C)
D)
Use the given graph to find the indicated limit.
45)
Find lim
x f(x).
45)
A)
3
B)
C)
4
D)
Solve the problem.
46)
A company is planning to manufacture a new blender. After conducting extensive market surveys,
the research department estimates a weekly demand of 600 blenders at a price of $50 per blender
and a weekly demand of 800 blenders at a price of $40 per blender. Assuming the demand equation
is linear, use the research department’s estimates to find the revenue equation in terms of the
demand x.
46)
A)
R(x) = 80x – 20x2
B)
R(x) = 20x +x2
20
C)
R(x) = 80x – 20
D)
R(x) = 80x –x2
20
Provide an appropriate response.
47)
Use a sign chart to solve the inequality. Express answers in interval notation.
– 5
–3x – 4 > 0
47)
A)
(0, )
B)
–, 4
3
C)
–, –3
4
D)
–4
3 ,
Use the definition f'(x) =lim
h
0f(x + h) – f(x)
h to find the derivative at x.
48)
f(x) = 4x + 9x3
48)
A)
4 + 9x2
B)
4 + 27x2
C)
4x + 27x2
D)
4x + 27x3
Find average rate of change for the function over the given interval.
49)
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.
49)
A)
4
B)
22
C)
9
D)
11
Solve the problem.
50)
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
9 , where 0 x 3. Approximate the
changes in body temperature produced by changing the drug dosage from 1 to 1.9 milligrams.
Round to the nearest hundredth when necessary.
50)
A)
3.17°F
B)
1.67°F
C)
0.22°F
D)
1.5°F
Use the graph to evaluate the indicated limit and function value or state that it does not exist.
51)
Find lim
x
0f(x) and f(0).
51)
A)
Does not exist; 6
B)
0; 6
C)
6; 0
D)
0; does not exist
Provide an appropriate response.
52)
Find f'(x) if f(x) = 3x4+ 6x7.
52)
A)
3x5+ 7x8
B)
12x3+ 42x6
C)
4x3+ 7x6
D)
7x3+ 13x6
Find the limit.
53)
Determine the limit.
lim
x –10 –f(x), where f(x) =1
x + 10
53)
A)
B)
0
C)
–1
D)
–
Provide an appropriate response.
54)
Find: d
dx 4
x4– 4 5x
54)
A)
16
x3– 204x
B)
1
x3–4
54x
C)
–16
x5–4
55x4
D)
–16
x3–4
54x
55)
Determine where the function f(x) =5x
2x – 3 is continuous.
55)
A)
–, 3
2
B)
(–, )
C)
–, 3
23
2,
D)
3
2,
56)
Find the slope of the secant line joining (2, f(2)) and (3, f(3)) for f(x) = –3x2– 8.
56)
A)
15
B)
–55
C)
–15
D)
55
57)
Find the vertical asymptote(s) of the graph of the given function.
f(x) =3x – 9
5x + 30
57)
A)
y = 8
B)
x = –6
C)
y = –3
D)
x = –8
58)
Use a sign chart to solve the inequality. Express answers in interval notation.
x2> 16
58)
A)
(–4, 4 )
B)
(–, –4) (4, )
C)
(4, )
D)
(–4, )
59)
If the limit at infinity exists, find the limit.
lim
x
3x3+ 5x
4x4+ 10x3+ 2
59)
A)
3
4
B)
C)
0
D)
1
60)
The revenue (in thousands of dollars) from producing x units of an item is modeled by
R(x) = 5x – 0.0005x2. Find the marginal revenue at x = 1000.
60)
A)
$4.50
B)
$4.00
C)
$10,300.00
D)
$104.00
The graph of a function f is given. Use the graph to answer the question.
61)
Use the graph of f given below to find f(-10).
10
-10 10
-10
61)
A)
16
B)
0
C)
6
D)
-10
Provide an appropriate response.
62)
Suppose that the total profit in hundreds of dollars from selling x items is given by P(x) =4x2– 5x
+ 10. Find the marginal profit at x = 5.
62)
A)
$45
B)
$35
C)
$32
D)
$15
The graph of y = f(x) is shown. Use the graph to answer the question.
63)
Is f continuous at x =-1.5?
63)
A)
Yes
B)
No
A
Provide an appropriate response.
64)
Use a graphing utility to find the discontinuities of the given rational function.
g(x) =x + 1
x3+ 2x2+ 10x – 13
64)
A)
3
B)
1
C)
–1
D)
Continuous at all values of x
B
Find the instantaneous rate of change for the function at the value given.
65)
Find the instantaneous rate of change for the function f(x) = 5x2+ x at x = – 4.
65)
A)
–14
B)
–39
C)
–41
D)
6
B
21
B
Find average rate of change for the function over the given interval.
66)
y =7x3+ 7x2+ 3 between x =-6 and x =-1
66)
A)
– 3
B)
– 1260
C)
3
5
D)
252
Provide an appropriate response.
67)
Solve the inequality and express the answer in interval notation: x2– 4x
x + 5 > 0.
67)
A)
(–5, )
B)
(–5, 0)
C)
(–5, 0) (4, )
D)
(4, )
Find average rate of change for the function over the given interval.
68)
y = x2+ 6x between x =5 and x =9
68)
A)
15
B)
135
4
C)
20
D)
80
9
Solve the problem.
69)
Suppose that the value V of a certain product decreases, or depreciates, with time t, in months,
where
V(t) = 100 –40t2
(t + 2) 2.
Find lim
t V(t).
69)
A)
80
B)
40
C)
100
D)
60
Find
y for the given values of x1 and x2.
70)
y = 2x + 3; x = 18, x = 0.5
70)
A)
0.5
B)
0.1
C)
5
D)
1
Provide an appropriate response.
71)
Use a graphing utility to approximate the partition numbers of the function to four decimal places:
f(x) =x4– 8x2– 4x + 1.
71)
A)
(–, –2.4976) (0.1832 , 3.0347)
B)
(–, –2.4976)
C)
(–, –2.4976) (–2.4976, –0.7203)
D)
(–, –2.4976) (–2.4976, –0.7203) (–0.7203, 0.1832 ) (0.1832 , 3.0347)
D
72)
If the limit at infinity exists, find the limit.
lim
x
5x2+ 7x – 9
– 6x2+ 2
72)
A)
0
B)
–5
6
C)
–2
9
D)
B
73)
Find: dy
dt if y =3t–4–5t–1
73)
A)
–12t–5+5t–2
B)
–12t–5–5t–2
C)
–12
t5–5
t2
D)
–12 t5– 5t2
A
D
74)
Find f'(x) if f(x) =.
74)
A)
f'(x) =2
B)
f'(x) = 0
C)
f'(x) = 1
D)
f'(x) =
Find the limit.
75)
Determine the limit.
lim
x
5+f(x), where f(x) =x2
(x – 5)3
75)
A)
–2
B)
5
C)
–
D)
D
Find the limit, if it exists.
76)
Find: lim
h
0
f(7 + h) – f(7)
h for f(x) = –x + 1.
76)
A)
0
B)
1
C)
–1
D)
Does not exist
C
Provide an appropriate response.
77)
Determine where the function H(x) =x2+ 7
x2+ x – 6 is continuous.
77)
A)
(–, –3) (–3, 2) (2, )
B)
(–, –3) (–3, 2)
C)
(–3, 2) (2, )
D)
(–, –3)
A
24
B
78)
Use the four step process to find f'(x) for the function f(x) =2
x2.
78)
A)
–2(h + 2x)
x2(x + h)2
B)
2(h + x)
x2(x + h)2
C)
–2(h + 2x + xh)
x2(x + h)2
D)
(h + 2x)
x2(x + h)2
79)
Find dy
dx for y =1
3x3+x7
10 .
79)
A)
1
9x2+7x6
10
B)
7x6
9x2+ 10
C)
–x–4+7
10x6
D)
–x–2+7
10x7
Solve the problem.
80)
Suppose that the value V of a certain product decreases, or depreciates, with time t, in months,
where
V(t) =37 –16t2
(t + 2) 2.
Find lim
t V(t).
80)
A)
37
B)
21
C)
16
D)
33
Provide an appropriate response.
81)
Use a sign chart to solve the inequality. Express answers in interval notation.
x2+ 6 < 2x
81)
A)
(2 , )
B)
C)
{2}
D)
(–, –2)
82)
Use a graphing utility to find the discontinuities of the given rational function.
g(x) =x + 1
x3+ 2x2+ 10x – 13
82)
A)
–1
B)
3
C)
1
D)
Continuous at all values of x
Use the given graph to find the indicated limit.
83)
lim
x
4+f(x)
83)
A)
B)
0
C)
D)
4
C
The graph of y = f(x) is shown. Use the graph to answer the question.
84)
Is f continuous at x =0?
84)
A)
No
B)
Yes
B
C
85)
Find the horizontal asymptote, if any, of the given function.
f(x) =(x – 3)(x + 4)
x2– 4
85)
A)
y = 3, y = –4
B)
y = 1
C)
x = 2, x = –2
D)
None
86)
Find f'(x) if f(x) = 9x7/5 – 5x2+ 10000.
86)
A)
f'(x) =63
5x2/5 – 10x
B)
f'(x) =63
5x6/5 – 10x + 4000
C)
f'(x) =63
5x6/5 – 10x
D)
f'(x) =63
5x2/5 – 10x + 4000
Find average rate of change for the function over the given interval.
87)
Find the average rate of change for f(x) =2x if x changes from 2 to 8.
87)
A)
2
B)
–3
10
C)
1
3
D)
7
Provide an appropriate response.
88)
Find the slope of the line tangent to the graph of the function at the given value of x.
y =x4+ 2x3+ 2x + 2 at x = –3
88)
A)
–52
B)
67
C)
–50
D)
65
Provide an appropriate response.
Find the limit, if it exists.
89)
Find: lim
x–1
6x + 5
5x – 6
89)
A)
–1
11
B)
1
11
C)
1
D)
–11
Provide an appropriate response.
90)
Evaluate dy and
y for y = f(x) =x2–7x + 5, x = 7, and dx =
x = 0.5.
90)
A)
dy = 3.75;
y = 3.75
B)
dy = 3.5;
y = 3.75
C)
dy = 3.75;
y = 3.5
D)
dy = 3.5;
y = 3.5
91)
The total profit from selling x units of doorknobs is P(x) =(6x – 7)(9x – 8). Find the marginal average
profit function.
91)
A)
P‘(x) = 54 –56
x2
B)
P‘(x) = 54x –111
C)
P‘(x) = 54x – 56
D)
P‘(x) = 54 –111
x2
Solve the problem.
92)
If an object moves along a line so that it is at y =f(x) =2x2– 7x – 6 at time x (in seconds), find the
instantaneous velocity function v = f'(x).
92)
A)
4x – 7
B)
2x – 7
C)
4x2– 7
D)
2x2– 7
Find the equation of the tangent line to the curve when x has the given value.
93)
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
93)
A)
y = 13x – 16
B)
y =1
20x +1
5
C)
y = – 39x – 80
D)
y = – 4
25 x +8
5
Provide an appropriate response.
94)
Find the horizontal asymptote, if any, of the given function.
f(x) =2x3– 3x – 9
9x3– 5x + 3
94)
A)
y = 0
B)
y =2
9
C)
y =3
5
D)
None
Find the limit, if it exists.
95)
Find: lim
x– 4
x2– 16
x + 4
95)
A)
–8
B)
8
C)
16
D)
– 24
Use the given graph to find the indicated limit.
96)
Find lim
x f(x).
96)
A)
B)
C)
4
D)
3
Solve the problem.
97)
The cost of renting a snowblower is $20 for the first hour (or any fraction thereof) and $5 for each
additional hour (or fraction thereof) up to a maximum rental time of 5 hours. Write a piecewise
definition of the cost C(x) of renting a snowblower for x hours. Is C(x) continuous at x = 2.5?
97)
A)
C(x) =
20 if 0 < x 1
25 if 1 < x 2
30 if 2 < x 3
35 if 3 < x 4
40 if 4 < x 5
; No
B)
C(x) =
25 if 0 < x 1
30 if 1 < x 2
35 if 2 < x 3
40 if 3 < x 4
45 if 4 < x 5
; No
C)
C(x) =
20 if 0 x 1
25 if 1 x 2
30 if 2 x 3
35 if 3 x 4
40 if 4 x 5
; No
D)
C(x) =
20 if 0 < x 1
25 if 1 < x 2
30 if 2 < x 3
35 if 3 < x 4
40 if 4 < x 5
; Yes
Provide an appropriate response.
98)
Given that f(x) =x
7 – x, find f –4
5. Express the answer as a simplified fraction.
98)
A)
–4
39
B)
–39
4
C)
4
39
D)
39
4
The graph of y = f(x) is shown. Use the graph to answer the question.
99)
Is f continuous at x =0?
99)
A)
No
B)
Yes
Find the limit, if it exists.
100)
Evaluate the following limit.
lim
x
2
1
x – 2
100)
A)
2
B)
C)
–
D)
Does not exist
Describe the end behavior of the function.
101)
f(x) = 5x4+ 5x + 11
101)
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) =
31
Solve the problem.
102)
Suppose an object moves along the y–axis so that its location is y = f(x) =x2+ x at time x (y is in
meters and x is in seconds). Find the average velocity (the average rate of change of y with respect
to x) for x changing from 2 to 9 seconds.
102)
A)
15 m/s
B)
3 m/s
C)
12 m/s
D)
84 m/s
Find the limit, if it exists.
103)
Given lim
x
5f(x) = 4 and lim
x
5 g(x) = –5, find lim
x
5
2f(x) + 3g(x)
3f(x) .
103)
A)
–7
12
B)
7
12
C)
–7
15
D)
7
15
104)
Find: lim
x
5
x – 5
x – 5
104)
A)
1
B)
0
C)
–1
D)
Does not exist
Provide an appropriate response.
105)
Find y’ if y =5
8.
105)
A)
1
B)
5
8x
C)
5
8
D)
0
106)
Find the values of x where the tangent line is horizontal for f(x) = 3x3– 2x2– 9.
106)
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 dy.
107)
y = x 5x + 1
107)
A)
15x + 2
5x + 1 dx
B)
15x – 2
5x + 1 dx
C)
15x + 2
2 5x + 1 dx
D)
15x – 2
2 5x + 1 dx
Provide an appropriate response.
108)
Find f'(x) for f(x) = 2x5+ 6x8.
108)
A)
2x4+ 6x7
B)
10x3+ 48x2
C)
10x6+ 48x9
D)
10x4+ 48x7
109)
Find: d
dx 4
x4– 5 3x
109)
A)
1
4x3–5
3x–2/3
B)
–16x–5–5
3x–2/3
C)
1
4x–5– 15x2/3
D)
1
x3+5
3x–4/3
List the x–values in the graph at which the function is not differentiable.
110)
110)
A)
x = –1
B)
x = 1
C)
x = 2
D)
x = 0
Provide an appropriate response.
111)
Find the equation of the tangent line at x = 2 for f(x) = 4 + x – 2x2– 3x3. Write the answer in the
form y = mx + b.
111)
A)
y = –47x + 68
B)
y = –39x + 52
C)
y = –43x + 48
D)
y = –43x + 60
112)
The total cost to produce x units of paint is C(x) = (5x + 3)(7x + 4). Find the marginal average cost
function.
112)
A)
C‘(x) = 35x + 41 +12
x
B)
C‘(x) = 70 –41
x
C)
C‘(x) = 70x + 41
D)
C‘(x) = 35 –12
x2
Find the limit, if it exists.
113)
Let f(x) =x2– 3x – 10
x + 2 . Find lim
x–2f(x).
113)
A)
5
B)
–2
C)
–7
D)
Does not exist
Provide an appropriate response.
114)
Find the equation of the tangent line at x = 7 for f(x) = 6 –x2. Write the answer in the form y = mx
+ b.
114)
A)
y = 14x – 55
B)
y = 7x + 55
C)
y = – 2x
D)
y = – 14x + 55
115)
y =5x2– 7x – 7
115)
A)
(10x – 7) dx
B)
10x dx
C)
10x – 14 dx
D)
10x – 7 dx
Use the graph to evaluate the indicated limit and function value or state that it does not exist.
116)
Find lim
x
0–f(x) and lim
x
0+f(x).
116)
A)
5; Does not exist
B)
–1; 5
C)
5; –1
D)
Does not exist; does not exist
Solve the problem.
117)
According to one theory of learning, the number of items, w(t), that a person can learn after t hours
of instruction is given by:
w(t) = 153t2,0 t 64
Find the rate of learning at the end of eight hours of instruction.
117)
A)
45 items per hour
B)
60 items per hour
C)
5 items per hour
D)
20 items per hour
118)
A cube 4 inches on an edge is given a protective coating 0.1 inches thick. About how much coating
should a production manager order for 900 cubes?
118)
A)
About 8640 in.3
B)
About 5760 in.3
C)
About 1440 in.2
D)
About 4320 in.2
Use the given graph to find the indicated limit.
119)
lim
x
5–f(x)
119)
A)
B)
0
C)
D)
5
Find the limit, if it exists.
120)
Given lim
x
4f(x) = –2 and lim
x
4 g(x) = 5, find lim
x
4
[g(x) – f(x)]
– 4 f(x) .
120)
A)
–7
8
B)
3
8
C)
7
8
D)
–3
8
Solve the problem.
121)
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+63i. Find the instantaneous rate of change of p with respect to i for i =0.9 A.
121)
A)
74.7 W/A
B)
72 W/A
C)
81 W/A
D)
64.8 W/A
Use the definition f'(x) =lim
h
0f(x + h) – f(x)
h to find the derivative at x.
122)
f(x) =10 – 14x2
122)
A)
10 – 28x
B)
10 – 14x
C)
–28x2
D)
–28x
Provide an appropriate response.
123)
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– 0.036x2+ 200x + 40,000
R(x) =450x
123)
A)
C'(x) =0.0012x2+ 0.072x + 200
R'(x) =450
P'(x) =0.0012x2+ 0.072x + 250
B)
C'(x) =0.0012x2– 0.072x + 200
R'(x) =450
P'(x) =-0.0012x2+ 0.072x + 250
C)
C'(x) =0.0012x2– 0.072x + 200
R'(x) =450
P'(x) =0.0012x2– 0.072x – 250
Answer Key
Testname: C2
Answer Key
Testname: C2
Answer Key
Testname: C2