Answer
Decreasing on: $(-\infty, -2), (2, \infty)$
Increasing on: $(-2,2)$
Work Step by Step
$h(x)=12x-x^{3}$, defined everywherre, continuous
$h^{\prime}(x)=12-3x^{2}$, differentiable everywhere
$=3(4-x^{2})$
$=3(2-x)(2+x)$
$3(2-x)(2+x) =0$
Critical numbers: $x=\pm 2$
$\left[\begin{array}{llll}
Interval & (-\infty,-2) & (-2,2) & (2,\infty)\\
\text{test point} & -3 & 0 & 3\\
f^{\prime}(\text{test point}) & -15 & 12 & -15\\
\text{sign} & - & + & -\\
& \searrow & \nearrow & \searrow
\end{array}\right]$
Decreasing on: $(-\infty, -2), (2, \infty)$
Increasing on: $(-2,2)$
