Thomas Calculus 13th [Solutions]

45. (a) y 6 x( x 1)( x 2)
(b)
3 2
6x 6x 12x y
and (2, ), falling on ( , 1) and (0, 2) a local maximum at 0,
2
2
1 7 1 7
x 2; y 18x 12x
12 6(3x
2x
2) 6 x x
3 3
the curve is concave up on
inflection at x
1 7
3
1 7
, and 1 7
3
3
Chapter 4 Practice Exercises 323
| | | the graph is rising on ( 1, 0)
1 0 2
x local minima at x 1 and
y
|
1 7
3
|
1 7
3
, , concave down on 1 7 , 1 7 points of
3 3
46 . (a)
(b)
2 2 3
y x (6 4 x) 6x 4x
y | | the curve is rising on , 3 , falling on
2
0 3/2
3
2 , a local maximum at 3
2
x ; y 12x 12x 12 (1 )
2 x x y | | concave
0 1
up on (0, 1), concave down on ( , 0) and (1, ) points of inflection at x 0 and x 1
47. (a)
(b)
y
4
x
2
2 x
2 2
x ( x 2) y | | | the curve is rising on , 2 and
2 0 2
2, , falling on 2, 2 a local maximum at x 2 and a local minimum at x 2;
y
3
4x 4x 4 x( x 1)( x 1) y | | | concave up on ( 1, 0) and (1, ),
1 0 1
concave down on ( , 1) and (0, 1) points of inflection at x 0 and x 1
48. (a)
2 4 2 2
y 4x x x (4 x ) y | | | the curve is rising on ( 2, 0) and (0, 2),
2 0 2
3
falling on ( , 2) and (2, ) a local maximum at x 2, a local minimum at x 2; y 8x 4x
2
4 x (2 x ) y | | | concave up on , 2 and 0, 2 , concave
2 0 2
down on 2, 0 and 2, points of inflection at x 0 and x 2
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