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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 $x=-3$.

I. $f(-3)$ exists.

II. $f’(-3)$ exists.

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

II only.

I and II only.

I, II, and III.

None of the statements are true.