Answer
The critical numbers are:
$x = -2.1$
$x = -1.3$
$x = -0.2$
$x = 1.3$
$x = 2.3$
Work Step by Step
$f(x) = \vert 1+5x-x^3 \vert$
On the graph we can see two local maxima where $f'(0) = 0$
Using the zoom function on a graphing calculator, we can estimate that these two critical numbers are $x = -1.3$ and $x = 1.3$
On the graph we can see three points which meet the x-axis at sharp points. At these three points, $f'(x)$ is undefined.
Using the zoom function on a graphing calculator, we can estimate that these three critical numbers are $x = -2.1, x = -0.2,$ and $x = 2.3$
