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The graph of the function $f$ shown in the figure below has a vertical tangent at the point $(2,0)$ and horizontal tangents at the points $(0,2)$ and $(4,-2)$.

For what values of $x, \hspace{.2cm} -6 \lt x \lt 6$, is $f$ not differentiable?

A

$-2$

B

$-2$ and $2$

C

$-2$, $0$, $2$, and $4$

D

$-2$, $0$, and $4$

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