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A function $f(x)$ is given below. Which of the following is true for $f(x)$?

$f(x) = \left\{ {\begin{array}{*{20}{c}} x&{x < 0}\\\ 0&{x = 0}\\\ {\sin x}&{0 < x < \frac{\pi }{2}}\\\ 1&{x \ge \frac{\pi }{2}} \end{array}} \right.$

I. $f(x)$ is continuous and differentiable at $x=0$.
II. $f(x)$ is differentiable at $x=\cfrac {\pi}{2}$.
III. $f(x)$ is continuous at $x = 0$ and at $x=\cfrac {\pi}{2}$.

A

I only.

B

II only.

C

II and III only.

D

I, II, and III.

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