Find dy/dx by implicit differentiation.
117)
x + y
x – y = x2+ y2
117)
A)
x(x – y)2+ y
x + y(x – y)2
B)
x(x – y)2+ y
x – y(x – y)2
C)
x(x – y)2– y
x – y(x – y)2
D)
x(x – y)2– y
x + y(x – y)2
Solve the problem.
118)
A tumor is approximately spherical in shape. If the radius of the tumor changes from 4 mm to
7 mm, find the approximate change in volume. Round your answer to the nearest hundred.
118)
A)
600 mm3
B)
1900 mm3
C)
100 mm3
D)
200 mm3
119)
P(x) = – x3+27
2x2– 60x + 100, x
5 is an approximation to the total profit (in thousands of dollars)
from the sale of x hundred thousand tires. Find the number of hundred thousands of tires that must
be sold to maximize profit.
119)
A)
5.5 hundred thousand
B)
4 hundred thousand
C)
4.5 hundred thousand
D)
5 hundred thousand
Use the differential to approximate the quantity to four decimal places.
120)
8.05
120)
A)
2.6833
B)
2.0500
C)
3.1583
D)
2.8417
33
Solve the problem.
121)
A zoom lens in a camera makes a rectangular image on the film that is 6 cm ×3 cm. As the lens
zooms in and out, the size of the image changes. Find the rate at which the area of the image begins
to change (dA/df) if the length of the frame changes at 0.6cm/s and the width of the frame changes
at 0.4 cm/s.
121)
A)
4.8 m2/s
B)
4.2 m2/s
C)
1.4 m2/s
D)
2 m2/2
122)
Find two numbers whose sum is 490 and whose product is as large as possible.
122)
A)
10 and 480
B)
1 and 489
C)
245 and 245
D)
244 and 246
Find the equation of the tangent line at the given point on the curve.
123)
2xy – y2= 1; (1, 1)
123)
A)
y = x – 1
B)
y = – x + 1
C)
x = 1
D)
y = 1
Solve the problem.
124)
A spherical balloon is being inflated. Find the approximate change in volume if the radius
increases from 6.3 cm to 6.4 cm.
124)
A)
158.76 cm3
B)
333.4 cm3
C)
0.252 cm3
D)
15.876 cm3
Find dy for the given values of x and x.
125)
y = x3+ 2x; x = 2, x = 0.01
125)
A)
0.07
B)
0.007
C)
0.14
D)
0.014
34
Solve the problem.
126)
The weight of a ram can be estimated by the function W(t) = – 7.3 + 304.8e–e(–0.00956(t – 131.9)),
where t is the age of the ram (in days) and W(t) is the weight of the ram (in kg). If a particular ram is
70 days old, use differentials to estimate how much weight it will gain before it is 100 days old.
126)
A)
16.4 kg
B)
28.5 kg
C)
30.5 kg
D)
25.9 kg
127)
The stadium vending company finds that sales of hot dogs average 34,000 hot dogs per game when
the hot dogs sell for $2.50 each. For each 50 cent increase in the price, the sales per game drop by
5000 hot dogs. What price per hot dog should the vending company charge to realize the maximum
revenue?
127)
A)
$2.95
B)
$0.90
C)
$3.20
D)
$3.40
Use the differential to approximate the quantity to four decimal places.
128)
e0.179
128)
A)
1.196
B)
1.1790
C)
0.8361
D)
.8210
Solve the problem.
129)
Of all numbers whose difference is 10, find the two that have the minimum product.
129)
A)
20 and 10
B)
5 and –5
C)
0 and 10
D)
1 and 11
Find the equation of the tangent line at the given value of x on the curve.
130)
3x2+ 4xy + y2+ x – 2y = – 7, x = – 1
130)
A)
y = – x + 3
B)
y = – x – 1
C)
x = – 1
D)
y = 3
35
Solve the problem.
131)
A book publisher wants to know how many times a year a print run should be scheduled. Suppose
it costs $5000 to set up the printing process, and the subsequent cost per book is so low it can be
ignored. Suppose further that the annual warehouse cost is $3 times the maximum number of
books stored. Assuming 5000 copies of the book are needed per year how many books should be
printed in each print run?
131)
A)
913
B)
1732
C)
2887
D)
4082
132)
An architect needs to design a rectangular room with an area of 64 ft2. What dimensions should he
use in order to minimize the perimeter?
132)
A)
16 ft ×16 ft
B)
8 ft ×16 ft
C)
8 ft ×8 ft
D)
12.8 ft ×64 ft
133)
The correlation between respiratory rate and body mass in the first three years of life can be
expressed by the function
log R(w) =1.89 – 0.47 log (w),
where w is the body weight (in kg) and R(w) is the respiratory rate (in breaths per minute). Find
R'(w) using implicit differentiation.
133)
A)
R'(w) =77.62w–1.47
B)
R'(w) = – 36.48w–1.47
C)
R'(w) = – 36.48w–0.53
D)
R'(w) = – 36.48w–0.47
134)
A local office supply store has an annual demand for 40,000 cases of photocopier paper per year. It
costs $4 per year to store a case of photocopier paper, and it costs $90 to place an order. Find the
optimum number of cases of photocopier paper per order.
134)
A)
1,800,000
B)
1342
C)
949
D)
424
Find dy for the given values of x and x.
135)
y =4
x4+ 3 x; x = 4, x = 0.5
135)
A)
47
128
B)
.45
C)
.47
D)
45
128
Solve the problem.
136)
One airplane is approaching an airport from the north at 206 km/hr. A second airplane approaches
from the east at 157 km/hr. Find the rate at which the distance between the planes changes when
the southbound plane is 27 km away from the airport and the westbound plane is 16 km from the
airport.
136)
A)
1208 km/hr
B)
257 km/hr
C)
86 km/hr
D)
1044 km/hr
Graph the function on the indicated domain, and use the capabilities of your calculator to find the location and value of
the indicated absolute extremum.
137)
f(x) = (x – 8)(x + 3); [0, )
Minimum
137)
A)
–30.25 at x =2.5
B)
–30.21 at x =2.7
C)
–29.89 at x =1.9
D)
–30.16 at x =2.2
Find the indicated absolute extremum as well as all values of x where it occurs on the specified domain.
138)
f(x) = (x2+ 4)2/3; [–2, 2]
Minimum
138)
A)
No absolute minimum
B)
2.924 at x = 1
C)
2.5198 at x = 0
D)
4 at x = 2
37
139)
f(x) = x2– 4; [–1, 2]
Maximum
139)
A)
0 at x = 2
B)
–3 at x = 1
C)
0 at x = – 2
D)
–3 at x = – 1
Find the location of the indicated absolute extremum for the function.
140)
Minimum
140)
A)
x = – 1
B)
x = 1
C)
x = 2
D)
x = – 2
Find dy/dx by implicit differentiation.
141)
yx + 1 = 4
141)
A)
y
2(x + 1)
B)
–y
2(x + 1)
C)
–2y
x + 1
D)
2y
x + 1
Find dy for the given values of x and x.
142)
y = 2x + 3; x = 18, x = 0.5
142)
A)
0.1
B)
1
C)
5
D)
0.5
38
Solve the problem.
143)
A company wishes to manufacture a box with a volume of 40 cubic feet that is open on top and is
twice as long as it is wide. Find the width of the box that can be produced using the minimum
amount of material.
143)
A)
3.6 ft
B)
7.2 ft
C)
3.2 ft
D)
6.4 ft
Find the location of the indicated absolute extremum for the function.
144)
Minimum
144)
A)
No minimum
B)
x = 1
C)
x = – 1
D)
x = 2
Solve the problem.
145)
Find the dimensions that produce the maximum floor area for a one–story house that is rectangular
in shape and has a perimeter of 148 ft.
145)
A)
74 ft ×74 ft
B)
12.33 ft ×37 ft
C)
37 ft ×148 ft
D)
37 ft ×37 ft
Find the location of the indicated absolute extremum for the function.
146)
Minimum
146)
A)
x = 2
B)
x = – 4
C)
x = 0
D)
x = – 3
147)
Maximum
147)
A)
No maximum
B)
x = 5
C)
x = 3
D)
x = 0
Find the equation of the tangent line at the given point on the curve.
148)
xy2= 4; (4, 1)
148)
A)
y = – 8x + 33
B)
y = – 1
8x +3
2
C)
y = – 2x + 9
D)
y = – 1
2x + 3
Answer Key
Testname: C6
Answer Key
Testname: C6
Answer Key
Testname: C6