Thomas Calculus 13th [Solutions]

52. The graph of the first derivative indicates that the curve is rising on
Chapter 4 Practice Exercises 325
17 33
0, and
16
17 33
, , falling on
16
17 33 17 33
17 33
17 33
( , 0) and , a local maximum at x , a local minimum at x . The derivative
16 16
16
16
approaches as x 0 and x 1, and approaches as x 0 , indicating a cusp and local minimum at
x 0 and a vertical tangent at x 1.
53. y x 1 1 4
x 3 x 3
54. y 2 x 2 10
x 5 x 5
55.
y x 2 1 1
x
x x
56.
y
x
2
x
x
1 x 1 1
x
57.
3 2
y x 2 x 1
2x
2 x
58.
y
4
x
x
1 2
x 1
x
2 2
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