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 \[x=1\]

Correct Answer: A

Solution :

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