James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

Appendix I Answers to Odd-Numbered Exercises A87
65. A. s2`, 1d ø s1, `d
B. y-int 0; x-int 0 C. None
D. VA x − 1; SA y − x 1 1
E. Inc on s2`, 0d, s2, `d;
dec on s0, 1d, s1, 2d
F. Loc max f s0d − 0;
loc min f s2d − 4
G. CU on s1, `d; CD on s2`, 1d
H. See graph at right.
67. A. s2`, 0d ø s0, `d
B. x-int 2s 3 4 C. None
D. VA x − 0; SA y − x
E. Inc on s2`, 0d, s2, `d;
dec on s0, 2d
F. Loc min f s2d − 3
G. CU on s2`, 0d, s0, `d
H. See graph at right.
_2
y
(0, 0)
y
(2, 3)
(2, 4)
y=x
69. A. R B. y-int 2
y
C. None
3 1
D. SA y − 1 1 1 {ln 2, + ln
2 x
2 2
2}
E. Inc on sln 2, `d;
2
dec on s2`, ln 2d
1
1
y=1+ x
F. Loc min f sln 2d − 3 2 1 1 2 ln 2
2
G. CU on s2`, `d
0 1
x
H. See graph at right.
71.
75. VA x − 0, asymptotic to y − x 3
y x π 2
y
0
y x π 2
x
2
0
y
10
10
0
ƒ
x
y=˛
2
x
x
3. Inc on s21.31, 20.84d, s1.06, 2.50d, s2.75, `d; dec on
s2`, 21.31d, s20.84, 1.06d, s2.50, 2.75d; loc max
f s20.84d < 23.71, f s2.50d < 211.02; loc min
f s21.31d < 20.72, f s1.06d < 233.12, f s2.75d < 211.33; CU
on s2`. 21.10d, s0.08, 1.72d, s2.64, `d; CD on s21.10, 0.08d,
s1.72, 2.64d; IPs s21.10, 22.09d, s0.08, 23.88d, s1.72, 222.53d,
s2.64, 211.18d
_2
50
_40
f
4
5. Inc on s2`, 21.47d, s21.47, 0.66d; dec on s0.66, `d;
loc max f s0.66d < 0.38; CU on s2`, 21.47d, s20.49, 0d,
s1.10, `d; CD on s21.47, 20.49d, s0, 1.10d;
IPs s20.49, 20.44d, s1.10, 0.31d, s0, 0d
_4
f
xÅ_1.47
3
_3
3
7. Inc on s21.40, 20.44d, s0.44, 1.40d; dec on s2, 21.40d,
s20.44, 0d, s0, 0.44d, s1.40, d; loc max f s20.44d < 24.68,
f s1.40d < 6.09; loc min f s21.40d < 26.09, f s0.44d < 4.68;
CU on s2, 20.77d, s0, 0.77d; CD on s20.77, 0d, s0.77, d;
IPs s20.77, 25.22d, s0.77, 5.22d
Exercises 4.6 • page 329
1. Inc on s2`, 21.50d, s0.04, 2.62d, s2.84, `d; dec on
s21.50, 0.04d, s2.62, 2.84d; loc max f s21.50d < 36.47,
f s2.62d < 56.83; loc min f s0.04d < 20.04, f s2.84d < 56.73;
CU on s20.89, 1.15d, s2.74, `d; CD on s2`, 20.89d, s1.15, 2.74d;
IPs s20.89, 20.90d, s1.15, 26.57d, s2.74, 56.78d
_3
60
150
_100
f
f
5
_0.2
1
_1
f
0.3
_π
f
8
_8
π
9. Inc on s28 2 s61, 28 1 s61d; dec on s2`, 28 2 s61d,
s28 1 s61, 0d, s0, `d; CU on (212 2 s138, 212 1 s138 ),
s0, `d; CD on (2`, 212 2 s138 ), s212 1 s138, 0d
f
1
f
75
55
2.3 3.3
_100 _1
0.95
_1 1
_10
ms30191-1
c3c 4.4.91-1
ms30191-2
c3c 4.4.91-2
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