Thomas Calculus 13th [Solutions]

228 Chapter 4 Applications of Derivatives
67.
1 2
y cos ( x ) y 1 (2 x ) 2x
, which
2 2 4
1 ( x ) 1 x
is zero at x = 0; an absolute maximum value is 2
at
x = 0; an absolute minimum value is 0 at x = 1 and
x = 1.
68.
sin 1 ( x ) 1 ( x
y e y e ) e , which
x 2 2x
1 ( e ) 1 e
is never zero; an absolute maximum value is 2
at
x = 0.
x
2/3 5 4
69. 2 1/3
x
y x (1) x ( x 2)
3 3
3 x
crit.pt. derivative extremum value
x 4
1/3
5 0 local max 12 10 1.034
25
x 0 undefined local min 0
70.
2/3 1/3 2
y x (2 x) 2 x ( x 4) 8x
8
3 3
3 x
2
crit.pt. derivative extremum value
x 1 0 minimum 3
x 0 undefined local max 0
x 1 0 minimum 3
71.
2
y x 1 ( 2 x) (1) 4 x
2
2 4 x
2 2 2
x (4 x ) 4 2x
2 2
4 x 4 x
crit.pt. derivative extremum value
x 2 undefined local max 0
x 2 0 minimum 2
x 2 0 maximum 2
x 2 undefined local min 0
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