I want calculate the maximum and minimum of the following function \begin{equation} f(x)=\Biggl\{ \begin{array}{c} \cos x \ \ \ \ \ x\in(0,\pi] \\ \sin x \ \ \ x\in[-\pi,0] \end{array} \end{equation} The points $x=-\pi/2$, $x=\pi$ are absolute minimum. Instead, the point $x=-\pi$ is a relative maximum. My question is: what happens in $ x = 0 $? It is not an absolute maximum. It can be a relative maximum?
Thank you very much.