Let $f$ be a function such that:

$$\lim \limits_{x \to -3^+} f'(x) =\lim \limits_{x \to -3^-} f'(x)$$

Which of the following must be true?

I.$f(-3)$ exists.

II.$f’(-3)$ exists.

III.$f(x)$ is continuous and differentiable at $x=-3$.

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