# Use the graph to determine each local extrema? (See Image)

Apr 29, 2017

Local maxima: $f ' \left(x\right)$ changes sign from positive to negative
$x = - 5 , x = 4$

Local minima: $f ' \left(x\right)$ changes sign from negative to positive
$x = 1$

#### Explanation:

A graph $f \left(x\right)$ has relative maxima or minima when the graph of $f ' \left(x\right)$ changes from positive to negative or negative to positive values.

This is because $f ' \left(x\right)$ represents the slope of $f \left(x\right)$ at any given $x$.

Note:
$f ' \left(- 3\right) = 0$, however, $x = - 3$ is not a relative extrema of the graph of $f \left(x\right)$ because $f ' \left(x\right)$ does not change sign.