CPM Homework Help : CALC Problem 3-102

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3-102.

Find $f ^\prime(x)$ for each of the following functions.

$f ( x ) = \frac { 2 } { 3 } ( x - 5 ) ^ { 3 } + x ^ { 2 }$
Answer (a):
$f '\left(x\right) = 2\left(x − 5\right)^{2} + 2x$

$f ( x ) = \sqrt [ 3 ] { x }$
Hint (b):
Before you find the derivative, rename $f(x)$ using laws of exponent.

$f ( x ) = \operatorname { sin } \frac { \pi } { 4 }$
Hint (c):
Careful. What is $\operatorname{sin}\frac{\pi }{4}$ ?
Describe the graph of $y=\text{ sin}\frac{\pi }{4}$ .
Describe the behavior of its slope.

$f ( x ) = \frac { 1 } { ( x + 1 ) ^ { 2 } }$
Hint (d):
Refer the the hint in part (b).

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