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Let $f(x)=\left\{\begin{array}{l}|x| & \text { for } 0<|x| \leq 2 \\ 0 & \text { for } x=0\end{array}\right.$ Then at x = 0, f has |
a local maximum no local maximum a local minimum no extremum |
no extremum |
$f(x)=\left\{\begin{array}{l}-x,-2<x<0 \\ 0, x=0 \\ x, 0<x<2\end{array}\right.$ f'(x) does not exist as f''(0–) = –1 and f'(0+) = 1. |
