Answer
$g(x)$ has three critical numbers : {$-2, 0, 2$}.
Work Step by Step
$g'(x)=4x^3-16x=4x(x^2-4)=4x(x-2)(x+2).$
$g'(x)=0\to 4x(x-2)(x+2)=0\to x=-2, x=0$ or $x=2.$
$g(x)$ has three critical numbers : {$-2, 0, 2$}.
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