Thomas Calculus 13th [Solutions]

Section 4.1 Extreme Values of Functions 221
22. f ( x) x 4 f ( x ) 1 no critical points;
f ( 4) 0, f (1) 5 the absolute maximum is 0
at x 4 and the absolute minimum is 5 at x 1
23.
2
f ( x) x 1 f ( x) 2x a critical point at
x 0; f ( 1) 0, f (0) 1, f (2) 3 the absolute
maximum is 3 at x 2 and the absolute minimum is
1 at x 0
24.
f ( x) 4
x
3
2
f ( x) 3x a critical point at
x 0; f ( 2) 12, f (0) 4, f (1) 3 the absolute
maximum is 12 at x 2 and the absolute
minimum is 3 at x 1
( 2, 12)
f ( x)
4 x
3
y
10
5
( 1, 3)
2 1 0 1
x
1 2 3 2
25. F ( x ) x F ( x ) 2 x , however
2 3
x
x
x 0 is not a critical point since 0 is not in the domain;
F(0.5) 4, F (2) 0.25 the absolute maximum
is 0.25 at x 2 and the absolute minimum is 4 at
x 0.5
1 1 2 1
26. F ( x ) ( ) ,
x
x F x x however
2
x
x 0 is not a critical point since 0 is not in the
domain; F( 2)
1
, F ( 1) 1 the absolute
2
maximum is 1 at x 1 and the absolute minimum
is 1 2 at x 2
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