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AP® Calculus AB-BC

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Moderate

Differentiability

APCALC-Z1E54U

All of the following statements are true EXCEPT

A

If a function is continuous at $x=c$, it must be differentiable at $x=c$

B

If a function is differentiable at $x=c$, then $\mathop {\lim }\limits_{x \to {c^ + }} f'(x) = \mathop {\lim }\limits_{x \to {c^ - }} f'(x)$

C

If $f(x)$ is differentiable at $x=c$, then $\mathop {\lim }\limits_{x \to {c^ + }} f(x) = \mathop {\lim }\limits_{x \to {c^ - }} f(x)=f(c)$

D

If a function is differentiable at $x=c$, it must be continuous at $x=c$