JEE Math Practice Question

Let $$f:[0,\infty ) \to [0,3]$$ be a function defined by $$f(x) = \left\{ {\begin{matrix} {\max \{ \sin t:0 \le t \le x\} ,} & {0 \le x \le \pi } \\ {2 + \cos x,} & {x > \pi } \\ \end{matrix} } \right.$$ Then which of the following is true?

1. A.f is continuous everywhere but not differentiable exactly at one point in (0, $$\infty$$)
2. B.f is differentiable everywhere in (0, $$\infty$$)
3. C.f is not continuous exactly at two points in (0, $$\infty$$)
4. D.f is continuous everywhere but not differentiable exactly at two points in (0, $$\infty$$)