Question

Let $f\left(x\right)=\{\begin{array}{cc}x+2,& -1\le x<0\\ 1,& x=0\\ \frac{x}{2},& 0<x\le 1\end{array}$
Then in $[-1,1],$ this function has

• A. a minimum
• B. a maximum
• C. either a maximum or a minimum
• D. neither a maximum nor a minimum

Answer 1

The correct option is D neither a maximum nor a minimum

$f\left(0\right)>f\left(0^{+}\right)$ and $f\left(0\right)<f\left(0^{-}\right)$. Hence, $x=0$ is neither a maximum nor a minimum