138)
A carpenter is building a rectangular room with a fixed perimeter of 200 ft. What are the
dimensions of the largest room that can be built? What is its area?
138)
A)
50 ft by 150 ft; 7500 ft2
B)
50 ft by 50 ft; 2500 ft2
C)
20 ft by 180ft; 3600 ft2
D)
100 ft by 100 ft; 10,000 ft2
139)
f(x) =x3+3x2– x – 24
139)
A)
(–1, 0)
B)
(–1, –21)
C)
(–1, 3)
D)
(1, 8)
140)
The annual revenue and cost functions for a manufacturer of precision gauges are approximately
R(x) =480x – 0.03x2 and C(x) =120x + 100,000, where x denotes the number of gauges made. What
is the maximum annual profit?
140)
A)
$1,280,000
B)
$1,080,000
C)
$1,180,000
D)
$980,000
141)
Goes through (0, –2) and has a local maximum at (1, 3)
141)
A)
f(x) = – 5x2+ 10x + 2
B)
f(x) = – 5x2– 6x – 2
C)
f(x) = – 5x2+ 10x – 2
D)
f(x) =5x2– 10x – 2
142)
Compute the maximum product for two positive numbers with the property that the sum of the
first plus five times the second is 5000.
142)
A)
25,000
B)
1,250,000
C)
50,000
D)
600
E)
none of these
143)
A rectangular corral with a total area of 60 square meters is to be fenced off and then divided into 2
rectangular sections by a fence down the middle.
The fencing for the outside costs $9 per running meter, whereas that for the interior dividing fence
costs $12 per running meter. Which of the following statements hold, if the cost (c) of the fencing is
to be maximized?
(I) The constraint equation is 3w + 2 l = 60 .
(II) The objective equation is 2l · w = 60 .
(III) The constraint equation is w · l = 60 .
(IV) The objective equation is C = 30w + 18l .
(V) The constraint equation is C = 12w + 9wl .
(VI) The objective equation is C = 60 – lw .
143)
A)
V and VI
B)
I and II
C)
III and IV
D)
none of these
144)
The cost of a computer system increases with increased processor speeds. The cost C of a system as
a function of processor speed is estimated as C =11S2– 9S + 1700, where S is the processor speed in
MHz. Find the processor speed for which cost is at a minimum. Round to the nearest tenth if
necessary.
144)
A)
0.5 MHz
B)
0.4 MHz
C)
3.3 MHz
D)
8.2 MHz
145)
The graph on the left shows the population (in millions) of a colony of bacteria after t hours as
given by the function f(t). The graph on the right shows f(t).
100 y = f(t)
60
20
2 4 6 8
12
y =f(t)
8
4
2 4 6 8
After how many hours was the population 30 million?
145)
A)
1 hr
B)
6 hr
C)
4 hr
D)
2 hr
146)
Compute the maximum product for two positive numbers with the property that the sum of the
first plus three times the second is 3000.
146)
A)
25,000
B)
750,000
C)
15,000
D)
30,000
E)
none of these
147)
Which of the following is (are) true of f(x) =x3– 3x2+ 3x?
(I) f increasing on (1, )
(II) (1, 1) is a relative extreme point
(III) (1, 1) is an inflection point
(IV) f is concave up on ( , 1)
147)
A)
I, II, and III
B)
I and III
C)
II, III, and IV
D)
I, II, and IV
E)
all of these
148)
f(x) =x3–4x2
148)
A)
B)
C)
D)
149)
f(x) =x3– 12x + 3
149)
A)
Relative minimum at (–2, 19); relative maximum at (2, –13)
B)
Relative maximum at (5, 68); relative minimum at (–3, 12)
C)
Relative maximum at (5, 68); relative minimum at (2, –13)
D)
Relative maximum at (–2, 19); relative minimum at (2, –13)
150)
f(x) =2x2+4x + 1
150)
A)
B)
C)
D)
151)
f(x) = – x2+5– 8x
151)
A)
(4 +21, 0)
B)
(–4±21, 0)
C)
(–4±221, 0)
D)
(–1±21, 0)
152)
In planning a sidewalk cafe, it is estimated that if there are 28 tables, the daily profit will be $8 per
table and that, if the number of tables is increased by x, the profit per table will be reduced by 1
4x
dollars (due to overcrowding). How many tables should be present in order to maximize the
profit?
152)
A)
10
B)
20
C)
30
D)
can’t do the problem without cost information
153)
A company is constructing an open–top, square–based, rectangular metal tank that will have a
volume of 37.5 ft3. What dimensions yield the minimum surface area? Round to the nearest tenth,
if necessary.
153)
A)
4.8 ft by 4.8 ft. by 1.6 ft
B)
4.2 ft by 4.2 ft. by 2.1 ft
C)
8.7 ft by 8.7 ft. by 0.5 ft
D)
3.3 ft by 3.3 ft. by 3.3 ft
154)
f(x) =4x3+ 2x +3
154)
A)
(0, 2)
B)
(3, 0)
C)
(0, 3)
D)
(2, 0)
155)
At which labeled point(s) is the graph concave down?
155)
A)
A, F
B)
A, B, F
C)
B
D)
A, B
156)
A book publisher wants to know how many times a year a print run should be scheduled. Suppose
it costs $2000 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 6000 copies of the book are needed per year how many books should be
printed in each print run?
156)
A)
2828
B)
632
C)
1000
D)
2000
157)
Find the x coordinates of all relative extreme points of f(x) =2
3x3– 7x2+ 24x – 72
157)
A)
x = – 4, –3
B)
x = – 4, –3, 0
C)
x = 0, 3, 4
D)
x = 3, 4
E)
x = 2, 6
158)
Find the inflection point(s) of f(x) =x3
3–5
2x2+ 6x – 36.
158)
A)
(10, f (10))
B)
(2, f(2)) and (3, f(3))
C)
5
2, f 5
2
D)
x = – 2, –3
E)
2
5, f 2
5
159)
f(x) =7x –x3
159)
A)
(1, 7)
B)
(0, 0), (1, 7)
C)
(0, 0)
D)
No points of inflection exist
160)
f(x) = 2x3+ 15x2+ 24x
160)
A)
Rel max: (0, 0), Rel min: (–8, 512)
Inflection point: (–4, 256)
B)
Rel max (–4, 16), Rel min: (–1, –11)
Inflection point: –5
2, 5
2
C)
Rel min: (3, 6)
No inflection points
D)
No extrema
Inflection point: (0, 0)
161)
Find the x coordinates of all relative extreme points of f(x) =2
3x3– 7x2+ 24x – 72
161)
A)
x = 2, 6
B)
x = 0, 3, 4
C)
x = – 4, –3
D)
x = 3, 4
E)
x = – 4, –3, 0
162)
At which labeled point(s) is the function increasing?
162)
A)
A, E
B)
C, F
C)
E
D)
A
163)
T(t) is the temperature on a cold day at time t hours. If T (5) = – 8, by approximately how much will
the temperature drop from 5:00 to 5:15?
163)
A)
3 degrees
B)
2 degrees
C)
1.25 degrees
D)
8 degrees
164)
Determine which function is the derivative of the other.
164)
A)
g(x) =f(x)
B)
f(x) =g(x)
165)
Find the inflection point(s) of y = 2x3– 3x2– 12x + 17.
165)
A)
(2, –3)
B)
7
2, 24 and 1
2, 21
2
C)
1
2, 21
2 and –1
2, 22
D)
1
2, 21
2
E)
none of these