### Home > CALC > Chapter 5 > Lesson 5.1.3 > Problem5-25

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.

1. $f(x)$ 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.

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.

1. See the hint in part (a).