question_answer

Let \[f(x)={{x}^{3}}-{{x}^{2}}+x+1\] and\[g(x)=\left\{ \begin{align}   & \max \{f(t);0\le t\le x\};0\le x\le 1 \\  & (3-x)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1<x\le 2 \\ \end{align} \right.\]then

A)  \[g(x)\] is continuous and derivable in (0,2)

B)  \[g(x)\] is discontinuous at finite number of points in (0,2)

C)  \[g(x)\] is non-derivable at 2 points

D)  \[g(x)\] is continuous but non-derivable at one point