Let the function \) be defined as follows: = \) then \right. which of the follow

Let the function \( f(x) \) be defined as follows: \( f(x)= \) \( \left\{\begin{array}{cc}x^{3}+x^{2}-10 x & -1 \leq x<0 \\ \cos x & 0 \leq x<\frac{\pi}{2} \\ 1+\sin x & \frac{\pi}{2} \leq x \leq \pi\end{array}, \) then \right. which of the following statement(s) is/are correct This question has multiple correct options

• A. Local maximum at \( x=0 \)
• B. Local maximum at \( x=\frac{\pi}{2} \)
• C. Absolute maxima at \( x=-1 \)
• D. Absolute minima at \( x=\pi \)