Question

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

Answer 1

Local maxima: `f'(x)` changes sign from positive to negative
`x=-5, x=4`

Local minima: `f'(x)` changes sign from negative to positive
`x=1`

Explanation:

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

This is because `f'(x)` represents the slope of `f(x)` at any given `x`.

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