Thomas Calculus 13th [Solutions]

266 Chapter 4 Applications of Derivatives
63.
64.
65.
66.
2
y x( x 12) x x 2 3 x 2 3 ,
y | | | rising on 2 3, 0 and
2 3 0 2 3
2 3, , falling on , 2 3 and 0, 2 3 a local
maximum at x 0, local minima at
x 2 3; y
2
1 ( x 12) x(2 x)
3( x 2)( x 2),
y | | concave up on ( , 2) and (2, ),
2 2
concave down on ( 2, 2) points of inflection
at x 2
y ( x
2
1) (2x 3), y | | rising on
3/2 1
3
2 , , falling on , 3 no local maximum,
2
a local minimum at 3
2 ;
y 2( x 1)(2x 3) ( x
2
1) (2) 2( x 1)(3x
2),
y | | concave up on , 2 and (1,
3
2/3 1
),
concave down on 2
3 , 1 points of inflection at x 2 and
3
x 1
2 2 2
y (8x 5 x )(4 x) x(8 5 x)(4 x) ,
y | | | rising on 0, 8 , falling on
5
0 8/5 4
( , 0) and 8 5 , a local maximum at x 8
5 ,
a local minimum at x 0;
2 2
y (8 10 x)(4 x) (8x 5 x )(2)(4 x)( 1)
2
4(4 x)(5x 16x
8), y | | |
concave
up on
8 2 6
, and 8 2 6
5
5
8 2 6 8 2 6
5 5
, 4 , concave down on
8 2 6 8 2 6
8 2 6
, and (4, ) points of inflection at x and
5 5
5
x 4
y
2
( x 2 x)( x
2
5) x( x 2)( x
2
5) ,
y | | | rising on ( , 0) and (2, ),
0 2 5
falling on (0, 2) a local maximum at x 0,
a local minimum at x 2;
y (2x 2)( x
2
5)
2
2( x 2 x)( x 5)
2( x
2
5)(2x 8x
5), y | | |
5
4 6 4 6
2 2
concave up on 4 6 , 4 6 and (5, ), concave down on
2 2
x
4 6
, and 4 6
2
2
5
, 5 points of inflection at
4
4 6
x and
2
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