Answer
$ x=2$, $ x=-2$
Work Step by Step
The tangent line is horizontal when the slope is 0.
This implies that $ f'(x)=0$.
$ f'(x)=\frac{d}{dx}(12x-x^{3})=12\times\frac{d}{dx}(x)-\frac{d}{dx}(x^{3})$
$=(12\times1)-3x^{3-1}=12-3x^{2}$
$12-3x^{2}=0$ when $ x=2$ or $ x=-2$
