One-Sided Limits and Differentiability

Question

Let $$h$$ be a function defined on an open interval containing $$x = 3$$. Given that $$\displaystyle\lim\limits_{x 	o 3^-} \frac{h(x) - h(3)}{x - 3} = 7$$ and $$\displaystyle\lim\limits_{x 	o 3^+} \frac{h(x) - h(3)}{x - 3} = 7$$, which of the following statements must be true?

Accepted Answer

$$h$$ is differentiable at $$x = 3$$ and $$h'(3) = 7$$.

Answer

$$h(3) = 7$$.

Answer

$$h$$ is increasing at $$x = 3$$.

Answer

$$\displaystyle\lim\limits_{x 	o 3} h(x) = 7$$.

One-Sided Limits and Differentiability

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