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Which of the following functions is differentiable at $x=2$?

A

$f(x)=|x-2|$

B

$f(x)=\cfrac{1}{x-2}$

C

$f(x) = \left\{ \begin{array}{ll} 4x-4 & x \leq 2 \\\ x^2 & x>2 \end{array} \right.$

D

$f(x)=\sqrt[3]{x-2}$

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