Question

Let $f\left(x\right)=|x|,$ for $0<|x|<2$
$=1,$ for $x=0$
Then, at $x=0,f\left(x\right)$ has

• A. A local maximum
• B. A local minimum
• C. No local maximum
• D. No extremum

Answer 1

The correct option is A A local maximum

$f\left(x\right)=\left|x\right|0<\left|x\right|<2$

$=1x=0$

Plotting $f\left(x\right)$ we get

(Image)

at $x=0,f\left(x\right)=1$

And clearly it will be a local maximum.