Limits Continuity and Differentiability

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