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AP® Calculus AB-BC

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Mean Value Theorem: Reasons for Failure

APCALC-HUHNLH

For which of the following reasons does the function $f\left( x \right) =\left| x \right| $ FAIL to satisfy the conditions of the Mean Value Theorem on the interval $[-5,5]$?

A

$f(0)=0$

B

$f(x)$ is discontinuous on $[-5,5]$.

C

$f^{ \prime }\left( 0 \right) =0$

D

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