Find the derivative.
130)
y = (4x + 3)5
130)
A)
dy
dx = 5(4x + 3)4
B)
dy
dx = 4(4x + 3)4
C)
dy
dx = (4x + 3)4
D)
dy
dx = 20(4x + 3)4
131)
y =ex
ln x
131)
A)
x ex ln x –ex
x ln2x
B)
x ex
C)
ex– x ex ln x
x ln2x
D)
ex+ x ex ln x
x
Find an equation for the line tangent to given curve at the given value of x.
132)
y =x3
2; x =8
132)
A)
y =512x +96
B)
y =32x –512
C)
y =96x –512
D)
y =32x +512
Find f[g(x)] and g[f(x)].
133)
f(x) =1
x – 5 ; g(x) = x + 5
133)
A)
f[g(x)] = (5x – 24)/(x – 5)
g[f(x)] = 1/x
B)
f[g(x)] = x – 5
g[f(x)] = 1/(x + 5)
C)
f[g(x)] = 1/x
g[f(x)] = (5x – 24)/(x – 5)
D)
f[g(x)] = 1/(x + 5)
g[f(x)] = x – 5
Solve the problem.
134)
A(x) = – 0.015x3+ 1.05x gives the alcohol level in an average person’s bloodstream x hours after
drinking 8 oz of 100–proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Find
the rate of change of alcohol level with respect to time.
134)
A)
dA
dx = – 0.045x2+ 1.05
B)
dA
dx = – 0.045x3+ 1.05
C)
dA
dx = – 0.045x2+ 1.05x
D)
dA
dx = – 0.015x2+ 1.05
Find the derivative.
135)
g(x) =6x5+ x4– 6x2+ 7, find g'(–4)
135)
A)
7472
B)
7728
C)
7424
D)
–208
Solve the problem.
136)
Rats are not native to the islands off the western coast of South America. However, rats are often
introduced accidentally to an island by visiting ships. The population of introduced rats follows the
logistic function with k = 0.00022 and t in months. Assume that there are 8 rats initially and that the
maximum population size is 12,000. Find the rate of growth of the population after 5 months.
136)
A)
78 rats/month
B)
106 rats/month
C)
87 rats/month
D)
214 rats/month
Find the derivative.
137)
y =e2x2+ x
137)
A)
4xe2x + 1
B)
4xex2+ 1
C)
4xe2x2+ 1
D)
4xe + 1
34
Find the derivative of the function.
138)
y =log 55x +8
138)
A)
5
ln 5 (5x + 8)
B)
5 ln5
5x + 8
C)
5
ln 5
D)
5
2(ln 5)(5x + 8)
Find the derivative.
139)
y =
3
x2+ 3
x
139)
A)
dy
dx =x2+ 9
3x2(x2+ 3)2/3
B)
dy
dx =3
x2(x2+ 3)2/3
C)
dy
dx =
–x2– 9
3x2(x2+ 3)2/3
D)
dy
dx =
–3
x2(x2+ 3)2/3
140)
y =3x2
140)
A)
2x ln 3
B)
3x2 x ln 3
C)
3x2 2x ln x
D)
3x2 2x ln 3
Solve the problem.
141)
The body–mass index (BMI) is calculated using the equation BMI =703w
h2, where w is in pounds
and h is in inches. Find the rate of change of BMI with respect to weight for Sally, who is 65” tall
and weighs 120 lbs. If both Sally and her brother Jesse gain the same small amount of weight, who
will see the largest increase in BMI? Jesse is 69” tall and weighs 190 lbs.
141)
A)
19.967, Jesse
B)
19.967, Sally
C)
0.166, Sally
D)
0.166, Jesse
Find f[g(x)] and g[f(x)].
142)
f(x) =x –3; g(x) =6x2+5
142)
A)
f[g(x)] =6x2+5–3
g[f(x)] =6x +2
B)
f[g(x)] =6x –13
g[f(x)] =6x2+2
C)
f[g(x)] =6x2–3
g[f(x)] =6(x –3)2+5
D)
f[g(x)] =6x2+2
g[f(x)] =6x –13
Solve the problem.
143)
When a particular circuit containing a resistor, an inductor, and a capacitor in series is connected to
a battery, the current i (in amperes) is given by i =20e–3t(e2.6t – e–2.6t) where t is the time (in
seconds). Find the time at which the maximum current occurs. Round to the nearest tenth of a
second.
143)
A)
0.6 sec
B)
1.4 sec
C)
0.5 sec
D)
1.5 sec
144)
The total cost to produce x handcrafted wagons is C(x) =100 + 7x – x2+ 8x3. Find the marginal cost
when x =8.
144)
A)
4188
B)
4088
C)
1527
D)
1627
145)
Prairie dogs form an important part of the coyote’s diet. As coyotes are hunting for prairie dogs,
they must be careful to expend just the right amount of time at each burrow. If a coyote spends too
little time at each burrow, it catches very few prairie dogs per kilocalorie of energy expended.
Likewise, if the coyote spends too much time digging at a single burrow, it can expend a large
amount of energy per prairie dog caught. The relation between energy expended and time spent at
each burrow is approximated by E =1
t+20
t – 0.75 t2 for t > 0.75 minutes, where t is in minutes and
E is in kcal expended per prairie dog caught. How much time should a coyote spend at each
burrow to minimize the energy expended per prairie dog caught. (Hint: pay close attention to the
domain of the above function.)
145)
A)
.8 minutes
B)
2.0 minutes
C)
1.5 minutes
D)
10 minutes
Find the derivative of the function.
146)
y = ln 7x3–x2
146)
A)
7x – 2
7x2– x
B)
21x – 2
7x3– x
C)
21x – 2
7x2
D)
21x – 2
7x2– x
Let f(x) = 8x2– 5x and g(x) = 7x +
9.
Find the composite.
147)
g[f(–k)]
147)
A)
56k2– 35k + 9
B)
392k2– 973k + 603
C)
56k2+ 35k + 9
D)
392k2+ 973k + 603
Use the product rule to find the derivative.
148)
g(x) = (x–5+ 3)(x–3+ 5)
148)
A)
g'(x) = – 8x–9– 25x–6– 9x–4
B)
g'(x) = – 8x–9– 25x–4– 9x–4
C)
g'(x) = – 8x–9– 25x–6– 9x–2
D)
g'(x) = – 8x–7– 25x–6– 9x–4
Use the quotient rule to find the derivative.
149)
g(x) =x2+ 5
x2+ 6x
149)
A)
g'(x) =2x3– 5x2– 30x
x2(x + 6)2
B)
g'(x) =4x3+ 18x2+ 10x + 30
x2(x + 6)2
C)
g'(x) =x4+ 6x3+ 5x2+ 30x
x2(x + 6)2
D)
g'(x) =6x2– 10x – 30
x2(x + 6)2
37
Find the derivative of the function.
150)
y = log (5x – 7)
150)
A)
5
ln 10
B)
5x – 7
5 ln 10
C)
1
ln 10 (5x – 7)
D)
5
ln 10 (5x – 7)
Find an equation for the line tangent to given curve at the given value of x.
151)
y =x2–4; x =3
151)
A)
y =6x –13
B)
y =6x –26
C)
y =3x –13
D)
y =6x –22
A
Write the function as the composition of two functions f and g such that y = f[g(x)]).
152)
y =6+4x2
152)
A)
f(x) =
46+4x2, g(x) =
46+4x2
B)
f(x) =6+4x2, g(x) =x
C)
f(x) =x, g(x) =6+4x2
D)
f(x) =6+4x, g(x) = x
C
Find an equation for the line tangent to given curve at the given value of x.
153)
y =x2– x; x = – 2
153)
A)
y = – 5x +2
B)
y = – 5x +4
C)
y = – 5x –4
D)
y = – 5x –2
C
Solve the following.
154)
At what points on the graph of f(x) = 2x3–6x2–49x is the slope of the tangent line –1?
154)
A)
(0, 0), (–2, 58)
B)
(–4, –28), (–164, –106)
C)
(4, –164), (–2, 58)
D)
(4, –164), (1, –53)
C
D
Provide an appropriate response.
155)
If Q =108e0.7t what happens to Q and to Q’ as t increases?
155)
A)
Q increases and Q’ decreases.
B)
Q increases and Q‘ increases.
C)
Q decreases and Q’ decreases.
D)
Q decreases and Q’ increases.
Find the derivative.
156)
y =(x +5)3e–5x
156)
A)
–15(x +5)2e–5x
B)
(x +5)2(x +8) e–5x
C)
–(x +5)2(5x +22) e–5x
D)
–(x +5)2(5x +22) e–6x
Find the derivative of the function.
157)
y = ln (x + 9)3
157)
A)
3
x
B)
9
x + 9
C)
3
x + 3
D)
3
x + 9
Provide an appropriate response.
158)
True or false? If average cost is decreasing then the marginal cost must be decreasing.
158)
A)
False
B)
True
Solve the problem.
159)
In one city, 29% of all aluminum cans distributed will be recycled each year. A juice company
distributes 103,000 cans. The number still in use after time t, in years, is given by
N(t) =103,000(0.29)t.
Find N'(t).
159)
A)
N'(t) =103,000(ln 0.29)(0.29)t
B)
N'(t) =103,000(ln t)(0.29)t
C)
N'(t) =103,000(0.29)t
D)
N'(t) =103,000t(0.29)t–1
Find the derivative.
160)
y =e–x+ 1
ex
160)
A)
ex+ 2
e2x
B)
–ex+ 2
e2x
C)
ex– 2
e2x
D)
–ex– 2
e2x
40
Answer Key
Testname: C4
Answer Key
Testname: C4
Answer Key
Testname: C4
Answer Key
Testname: C4