• question_answer Let $f(x)=\,\left\{ \begin{matrix} \sin \,\frac{\pi x}{2},\,0\le \,x<1 \\ 3-2x,\,\,x\ge 1\, \\ \end{matrix}, \right.$ then A)  $f(x)$has local maxima at $x=1$ B)  $f(x)$has local minima at $x=1$ C)  $f(x)$doesn't have any local extrema at $x=1$ D)  $f(x)$has global minima at $x=1$

From graph, it is clear that, $f(x)$ has local maxima at $x=1$.