Continuity and Differentiability of a Piecewise Function
Let $$w$$ be the function defined by $$w(x) = \begin{cases} 2x + 3 & \text{if } x \leq 1 \\ x^2 + 1 & \text{if } x > 1 \end{cases}$$. Which of the following statements about the function $$w$$ is true?
A
$$w$$ is continuous and differentiable at $$x = 1$$.
B
$$w$$ is defined but neither continuous nor differentiable at $$x = 1$$.
C
$$w$$ is differentiable but not continuous at $$x = 1$$.
D
$$w$$ is continuous but not differentiable at $$x = 1$$.
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