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5-25.

Use the graphs of $f^\prime(x)$ and $g^\prime(x)$ below to determine the $x$ -values of all local minimums, maximums, and points of inflection.

Hint (a):
$f(x)$ will be increasing where $f^\prime(x)$ is positive, and vice versa.
$f(x)$ will be concave up where $f^\prime(x)$ has positive slopes, and vice versa.
Answer (a):
Local max at $x =-1$ ; $f^\prime(x)$ changes from positive to negative.
Inflection points at $x = -0.5$ , $0$ , $0.5$ ; $f^\prime(x)$ changes slope.
Local min at $x = 1$ ; $f^\prime(x)$ changes from negative to positive.

Hint (b):
See the hint in part (a).

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