Let $f:[0, \infty) \rightarrow[0,3]$ be a function defined by $\mathrm{f}(\mathrm{x})=\left\{\begin{array}{cc}\max \{\sin \mathrm{t}: 0 \leq \mathrm{t} \leq \mathrm{x}\}, & 0 \leq \mathrm{x} \leq \pi \\ 2+\cos \mathrm{x}, & \mathrm{x}>\pi\end{array}\right.$ Then which of the following is true ?
Select the correct option:
A
ƒ is continuous everywhere but not differentiable exactly at one point in $(0, \infty)$
B
ƒ is differentiable everywhere in $(0, \infty)$
C
ƒ is not continuous exactly at two points in $(0, \infty)$
D
ƒ is continuous everywhere but not differentiable exactly at two points in $(0, \infty)$
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