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For which of the following reasons does the function $f\left( x \right) ={ (x-1) }^{ \frac{2}{3} }$ FAIL to satisfy the conditions of the Mean Value Theorem on the closed interval $[-2,2]$?

A

$f^{ \prime }\left( 0 \right)$ does not exist.

B

$f^{ \prime }\left( 1 \right)$ does not exist.

C

$f\left( -2 \right) \neq f\left( 2 \right) $

D

$f\left( 1 \right) =0$

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