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All of the following statements are true EXCEPT

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

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

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

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