Find the derivative.
74)
y=x3
74)
A)
dy
dx =x3
B)
dy
dx =x2
C)
dy
dx =3x2
D)
dy
dx =3x3
Solve the problem.
75)
Refer to a line of slope m. If you begin at a point on the line and move h units in the x–direction,
how many units must you move in the y–direction to return to the line?
m =2
3, h =1
4
75)
A)
3
4
B)
6
C)
1
4
D)
1
6
D
76)
Which of the following properties are satisfied by the following function: f(x) =
x2+ 1 for x < 0
1for x = 0
5x + 1 for x > 0
(I) f(x) is continuous
(II) f(x) is differentiable for all x
(III) f(x) is differentiable at x = – 2
76)
A)
III only
B)
I, II, and III
C)
I and III only
D)
I only
E)
I and II only
C
Differentiate.
77)
f(x) =5x2+ 9x + 1
77)
A)
f(x) =10x2+ 9
B)
f(x) =10x + 9
C)
f(x) =5x + 9
D)
f(x) =5x2+ 9
B
17
C
Write an equation for the line described.
78)
Through (7, –5) and (0, –7)
78)
A)
y =12
7x – 7
B)
y = – 12
7x – 7
C)
y =2
7x – 7
D)
y = – 2
7x – 7
Provide an appropriate response.
79)
Is the function given by f(x) =
–5x + 10,for x < 1
1, for x = 1
3x – 9,for x > 1
continuous at x = 1? Why or why not?
79)
A)
No, lim
x
1f(x) does not exist
B)
Yes, lim
x
1f(x) = f(1)
A
80)
Let y = (–4 + 3 x)4. Compute dy
dx x = 4 .
80)
A)
–6
B)
24
C)
6
D)
27
16
E)
none of these
B
Write an equation for the line described.
81)
Through (–7, 0) and (0, –4)
81)
A)
y = – 7
4x – 4
B)
y =4
7x – 4
C)
y = – 4
7x – 4
D)
y =7
4x – 4
C
18
C
82)
For the following function g(x), determine whether or not lim
x–1g(x) exists. If so, give the limit.
82)
A)
3
B)
0
C)
–3
D)
does not exist
Find f'(x) at the given value of x.
83)
f(x) =x2– 9x – 1; Find f (–3).
83)
A)
–16
B)
–15
C)
35
D)
–6
Solve the problem.
84)
If the price (in dollars) of a product is given by P(x) =1024
x+ 1500, where x represents the demand
for the product, find the rate of change of price when the demand is 32 units.
84)
A)
$32/unit
B)
$1/unit
C)
–$1/unit
D)
–$32/unit
85)
Find the derivative of f(x) = 2 x at x = 4.
85)
A)
–1
2
B)
–1
C)
2
D)
1
2
Solve the problem.
86)
A ball is thrown vertically upward from the ground at a velocity of 126 feet per second. Its distance
from the ground after t seconds is given by s(t) = – 16t2+126t. How fast is the ball moving 4
seconds after being thrown?
86)
A)
–14 ft per sec
B)
–2 ft per sec
C)
248 ft per sec
D)
62 ft per sec
87)
Find the slope of the line with equation 3y + 2 = 5x – 2y?
87)
A)
1
B)
5
3
C)
–1
2
D)
5
Differentiate.
88)
y = (x2+2)3
88)
A)
dy
dx = 6x5+12x3+12x
B)
dy
dx = 6x5+24x3+24x
C)
dy
dx = 6x5+20x3+24x
D)
dy
dx = 3x5+24x3+24x
Solve the problem.
89)
The area A(r) =r2 of a circular oil spill changes with the radius. At what rate does the area change
with respect to the radius when r =3 ft?
89)
A)
9ft2/ft
B)
6ft2/ft
C)
6ft2/ft
D)
3ft2/ft
Differentiate.
90)
y =
4x3
90)
A)
dy
dx =43x
3
B)
dy
dx =3
44x
C)
dy
dx =1
4x
D)
dy
dx =34x
4
91)
Find the average rate of change for f(x) = – 2x2+ 5x – 2 on [–1, 1]
91)
A)
5
B)
0
C)
undefined
D)
3
E)
10
Determine the value of k that makes the function f(x) continuous at x = 0.
92)
f(x) =k(x2+ 9) for x
0
5+ x for x < 0
92)
A)
k =9
5
B)
k =5
9
C)
k =14
D)
k = – 5
9
93)
Find the derivative of f(x) =1
3x
.
93)
A)
2
3x–4/3
B)
–1
3x4/3
C)
5
3x2
D)
none of these
Differentiate.
94)
y = – 12 x
94)
A)
dy
dx = – 6
x
B)
dy
dx =6 x
C)
dy
dx = – 12
x
D)
dy
dx =6
x
95)
h(x) =5
x3–4x2+ 2
95)
A)
h'(x) =3x2– 8x
(x3– 4x2+ 2)2
B)
h'(x) =15x2– 40x
x3–4x2+ 2
C)
h'(x) =
–15x2+ 40x
(x3–4x2+ 2)2
D)
h'(x) =5
(3x2– 8x)2
Find f'(x) at the given value of x.
96)
f(x) = – 7x2+4x +5; Find f (7).
96)
A)
102
B)
–70
C)
–89
D)
–94
Differentiate.
97)
f(x) =4x4– 7x3– 3
97)
A)
f(x) = 4x3+ 3x2– 7
B)
f(x) = 4x3+ 3x2
C)
f(x) =16x3– 21x2
D)
f(x) =16x3– 21x2– 7
Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.
98)
lim
x
6x + 1
13x – 7
98)
A)
6
13
B)
C)
0
D)
–1
7
Provide an appropriate response.
99)
The tangent line to the curve y =x3+3x2–42x – 6 has slope 3 at two points on the curve. Find the
two points.
99)
A)
(5, 0); (–3, 0)
B)
(–5, 160); (3, –72)
C)
(–5, 154); (3, –78)
D)
(5, 154); (–3, –78)
C
100)
Find the equation of the following line: Parallel to 6x + y –6= 0; (5, 2) on line.
100)
A)
y = – 6x – 32
B)
y = – 1
6x –16
3
C)
y =6x – 32
D)
y = – 6x + 32
D
101)
Use the graph of f to determine if f is continuous at x = – 2.
101)
A)
no
B)
yes
A
A
Find f'(x) at the given value of x.
102)
f(x) = – 2x2+ 2x; Find f (8).
102)
A)
–16
B)
–192
C)
–23
D)
–30
Find the difference quotient f(x +
h) – f(x)
h and simplify.
103)
f(x) =x2+ 8x
103)
A)
2x + h + 1
B)
h + 8
C)
2xh + h + 8x
D)
2x + h + 8
Solve the problem.
104)
A line is specified by giving the slope and a point on the line. The first coordinate of another point
is given. Without deriving the equation of the line, find the second coordinate of the point.
Slope is 1, (2, 2) is on line. Find (4, __ ).
104)
A)
(4, 0)
B)
(4, 4)
C)
(4, 2)
D)
(4, –4)
105)
Find the equation of the following line: Parallel to y = – 1
7x +3; (5, 3) on line.
105)
A)
y = – 1
7x –26
7
B)
y = – 7x – 26
C)
y = – 1
7x +26
7
D)
y =1
7x –26
7
Use the properties of limits to help decide whether the limit exists. If the limit exists, find its value.
106)
lim
x
1
x2+8x –9
x –1
106)
A)
0
B)
8
C)
10
D)
Does not exist
Give an appropriate answer.
107)
Let lim
x –2f(x) = – 9 and lim
x –2g(x) = – 5. Find lim
x –2[f(x) – g(x)].
107)
A)
–14
B)
–4
C)
–2
D)
–9
Referring to the graph below, assign one of the following descriptors to the point: large positive slope, small positive
slope, zero slope, small negative slope, large negative slope.
108)
S
108)
A)
large positive slope
B)
large negative slope
C)
zero slope
D)
small negative slope
B
B
Solve the problem.
109)
The graph below shows the number of tuberculosis deaths in the United States from 1989 to 1998.
Deaths
Year
Estimate the average rate of change in tuberculosis deaths from 1991 to 1993.
109)
A)
About –80 deaths per year
B)
About –45 deaths per year
C)
About –30 deaths per year
D)
About –0.4 deaths per year
110)
Find the second derivative of f(x) =1
3x3/2 –4
3x1/4 + 5x – 2
110)
A)
x1/2 +4
9x–7/4
B)
1
4x–1/2 +1
4x–7/4
C)
1
2x1/2 –1
3x–3/4 + 5
D)
2
9x1/2 –16
3x–3/4 + 5
E)
1
4x–1/2 –1
4x–7/4
Solve the problem.
111)
The size of a population of mice after t months is P = 100(1 + 0.2t + 0.02t2). Find the growth rate at t
=21 months.
111)
A)
208 mice/month
B)
52 mice/month
C)
104 mice/month
D)
204 mice/month
Give an appropriate answer.
112)
Let lim
x –7f(x) = – 8 and lim
x –7g(x) = – 6. Find lim
x –7
f(x)
g(x) .
112)
A)
–2
B)
–7
C)
4
3
D)
3
4
Write an equation for the line described.
113)
Passes through (5, 3) with slope –2
9
113)
A)
y = – 2
9x +9
37
B)
y = – 2
9x +37
9
C)
y = – 2
9x –37
9
D)
y = – 9
2x –9
37
Differentiate.
114)
f(x) =2x – (x2+ 1)7
3
114)
A)
f'(x) =2–x
3(x2+ 1)6
B)
f'(x) = 2 – 7(x2+ 1)6
C)
f'(x) =2
3–14
3x(x2+ 1)6
D)
none of these
27
115)
y =4
x–x
3
115)
A)
dy
dx =4
x2–1
3
B)
dy
dx = – 4
x2+x
3
C)
dy
dx = – 4
x2–1
3
D)
dy
dx = – 4x –1
3
Find the average rate of change for the function over the given interval.
116)
y =8x3– 4x2– 6 between x = – 9 and x =2
116)
A)
42
11
B)
564
C)
21
D)
3102
117)
For the following function f(x), determine whether or not lim
x
0f(x) exists. If so, give the limit.
117)
A)
1
B)
0
C)
3
2
D)
does not exist
118)
Find the second derivative of y =1
2x + 3.
118)
A)
1
6x4
B)
–1
6x4
C)
–6x4
D)
2x0
E)
none of these
29
Answer Key
Testname: C1
30
Answer Key
Testname: C1
31
Answer Key
Testname: C1