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?