Continuity and Differentiability of a Piecewise Function

Question

Let $$h$$ be the function defined by $$h(x) = \begin{cases} -x^2 + 2x & 	ext{if } x \leq 1 \ x & 	ext{if } x > 1 \end{cases}$$. Which of the following statements about $$h$$ is true?

Accepted Answer

$$h$$ is continuous but not differentiable at $$x = 1$$.

Answer

$$h$$ is continuous and differentiable at $$x = 1$$.

Answer

$$h$$ is defined but neither continuous nor differentiable at $$x = 1$$.

Answer

$$h$$ is differentiable but not continuous at $$x = 1$$.

Continuity and Differentiability of a Piecewise Function

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