5128_ch04ansTE_pp652-661

Additional Answers 661
(c) Maximum volume 66.019 in 3 when x 1.962 in.
(d) V(x) 6x 2 – 50 x 75 which is zero at x 25 57
1.962.
6
(b)
y
2
70. (a) The only x-value for which f has a relative maximum is x – 2. That
is the only place where the derivative of f goes from positive to
negative.
(b) The only x-value for which f has a relative minimum is x 0. That is
the only place where the derivative of f goes from negative to positive.
(c) The graph of f is concave up on (1, 1) and on (2, 3). Those are the intervals
on which the derivative of f is increasing.
(d)
y
LRAM 1.25
2
x
6. (a)
2
y
–3 3
x
72. (a) V a 2 b, and b 60 2a
15 a 4
2 , so V 15pa2 p a 3 .
2
Thus d V
30pa 3p a 2
3 pa(20 a). The domain of consideration
da
2 2
for a in this problem is (0, 30), so a 20 is the only critical number.
The cylinder of maximum volume is formed when a 20 and b 5.
(b) The sign graph for the derivative d V
3 pa(20 – a) on the interval
da
2
(0, 30) is as follows:
x
0 20 30
By the First Derivative Test, there is a maximum at x 20.
(b)
2
y
RRAM 1.25
2
x
CHAPTER 5
2
x
Section 5.1
Exercises 5.1
5. (a) y
2
7.
MRAM 1.375
n LRAM n MRAM n RRAM n
10 1.32 1.34 1.32
50 1.3328 1.3336 1.3328
100 1.3332 1.3334 1.3332
500 1.333328 1.333336 1.333328
R
2
x
13.
14.
n
MRAM
10 526.21677
20 524.25327
40 523.76240
80 523.63968
160 523.60900
n error % error
10 2.61799 0.5
20 0.65450 0.125
40 0.16362 3.12 10 2
80 0.04091 7.8 10 3
160 0.01023 2 10 3