Thomas Calculus 13th [Solutions]

Section 4.3 Monotonic Functions and the First Derivative Test 245
47. (a)
2
g( x) x 4x 4 g ( x) 2x 4 2( x 2) a critical point at x 2
g(1) 1, g (2) 0 a local maximum is 1 at x 1, a local minimum is g(2) 0 at 2
(b) no absolute maximum; absolute minimum is 0 at x 2
(c)
g
[ | and
1 2
x
48. (a)
2
g( x) x 6x 9 g ( x) 2x 6 2( x 3) a critical point at x 3
g( 4) 1, g ( 3) 0 a local maximum is 0 at x 3, a local minimum is 1 at x 4
(b) absolute maximum is 0 at x 3; no absolute minimum
(c)
g
[ | and
4 3
49. (a)
3
f ( t) 12t t
f ( t) 12
2
3t 3(2 t)(2 t ) critical points at t 2 f [ | |
3 2 2
f local maxima are 9 at t 3 and 16 at t 2, a local minimum
and f ( 3) 9, f ( 2) 16, (2) 16
is 16 at t 2
(b) absolute maximum is 16 at t 2; no absolute minimum
(c)
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