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

Appendix I Answers to Odd-Numbered Exercises A83
31. y
y=8
(d)
y
10
5
(2, 5)
5
(0, 3)
33. (a) No
(b) Yes
(c)
IP
0 x
2
IP
y
-1 0 1 2 x
y
4
4
IP
IP
_2
_5
(_2, _5)
0 2 x
IP IP
(2, _5)
41. (a) Inc on s2`, 22d, s0, `d;
dec on s22, 0d
(b) Loc max hs22d − 7;
loc min hs0d − 21
(c) CU on s21, `d;
CD on s2`, 21d; IP s21, 3d
(d) See graph at right.
43. (a) Inc on s2`, 4d;
dec on s4, 6d
(b) Loc max F s4d − 4s2
(c) CD on s2`, 6d; No IP
(d) See graph at right.
(_2, 7)
y
(_1, 3)
_1
y
7
(0, _1)
{ 4, 4œ„2 }
Stewart / Calculus: ms80622-1ET 5 th Editio n
Solution Ar 6et t 4.3.37
5et040341 07.30.06
5.24.02
0 4 6 x
x
-1 0 1 2 x
35. (a) Inc on (0, 2), (4, 6), s8, `d;
dec on (2, 4), (6, 8)
(b) Loc max at x − 2, 6;
loc min at x − 4, 8
(c) CU on (3, 6), s6, `d;
CD on (0, 3) (d) 3
(e) See graph at right.
37. (a) Inc on s2`, 22d, s2, `d; dec on s22, 2d
(b) Loc max f s22d − 18; loc min f s2d − 214
(c) CU on s0, `d, CD on s2`, 0d; IP s0, 2d
(d)
(_2, 18)
y
y
0 2 4 6 8
x
45. (a) Inc on s21, `d;
dec on s2`, 21d
(b) Loc min Cs21d − 23
(c) CU on s2`, 0d, s2, `d;
CD on s0, 2d;
IPs s0, 0d, (2, 6s 3 2 )
(d) See graph at right.
47. (a) Inc on s, 2d;
dec on s0, d
(b) Loc min fsd − 21
(c) CU on sy3, 5y3d;
CD on s0, y3d, s5y3, 2d;
IPs sy3, 5 4d, s5y3, 5 4d
(d) See graph at right.
y
1
y
_4 0
(_1, _3)
π 5
”
3
,
4
’
{2, 6 Œ„2}
0 π 2π ¨
_1
(π, _1)
x
5π 5
”
3
,
4
’
2
_2 0 2
(2, _14)
39. (a) Inc on s22, 0d, s2, `d; dec on s2`, 22d, s0, 2d
(b) Loc max f s0d − 3; loc min f s62d − 25
(c) CU on S2`, 2 S
s3D, 2 2
s3 , `D; CD on S2 2
s3 , 2
s3D;
IPs S6 D
2
s3 , 2 13 9
x
49. (a) VA x − 0; HA y − 1 y
(b) Inc on s0, 2d;
y=1
dec on s2`, 0d, s2, `d
(c) Loc max f s2d − 5 4
(d) CU on s3, `d;
CD on s2`, 0d, s0, 3d; IP s3, 11 9 d
(e) See graph at right.
51. (a) HA y − 0
(b) Dec on s2`, `d
(c) None
(d) CU on s2`, `d
(e) See graph at right.
ms80628-1 (2, 5/4)
3c3 4.3.43
7.31.06
0 2 3
y
1
0
x
x
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