A function is defined as follows: = \) ^{2} & \text { for } \frac{\pi}{2} \leq x

A function \( f \) is defined as follows: \( \boldsymbol{f}(\boldsymbol{x})= \) \( \left\{\begin{array}{ll}1 & \text { for }-\infty< \\ 1+\sin x & \text { for } 0 \leq x<\frac{\pi}{2} \\ 2+\left(x-\frac{\pi}{2}\right)^{2} & \text { for } \frac{\pi}{2} \leq x<+\infty\end{array}\right. \) Discuss the continunity and differentiability at \( \boldsymbol{x}=\mathbf{0} \& \boldsymbol{x}=\boldsymbol{\pi} / \mathbf{2} \) This question has multiple correct options

• A. continuous but not differentiable at \( x=0 \)
• B. differentiable and continuous at \( x=\pi / 2 \)
• C. neither continuous but nor differentiable at \( x=0 \)
• D. continuous but not differentiable at \( x=\pi / 2 \)