APFIVE Differentiability of a Piecewise Function
Let $$v$$ be the function defined by $$\displaystyle v(x) = \begin{cases} \sqrt{x+6} & \text{if } x < 3 \\ 2x - 3 & \text{if } x \geq 3 \end{cases}$$. Which of the following statements about $$v$$ is true?
I. $$\displaystyle \lim_{x \to 3^-} v(x) = \lim_{x \to 3^+} v(x)$$
II. $$\displaystyle \lim_{x \to 3^-} v'(x) = \lim_{x \to 3^+} v'(x)$$
III. $$v$$ is differentiable at $$x = 3$$.
A
None
B
I only
C
I, II, and III
D
II and III only
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