Which of the Following Properties Are Satisfied by the Following $\left\{ \begin{array} { l l } x ^ { 2 } + 1 & \text { for } x < 0 \\1 & \text { for } x = 0 \\5 x + 1 & \text { for } x > 0\end{array} \right.$

Multiple Choice

Which of the following properties are satisfied by the following function: f(x) = $\left\{ \begin{array} { l l } x ^ { 2 } + 1 & \text { for } x < 0 \\1 & \text { for } x = 0 \\5 x + 1 & \text { for } x > 0\end{array} \right.$ (I) f(x) is continuous
(II) f(x) is differentiable for all x
(III) f(x) is differentiable at x = -2

A) III only
B) I only
C) I, II, and III
D) I and II only
E) I and III only