If $f(x)=x^2;x \in (-2, 3),$ then absolute maximum and absolute minimum values (if any) are :

Absolute maximum does not exist,  absolute minimum =0.

The correct answer is Option (2) → Absolute maximum does not exist,  absolute minimum = 0.

$f(x)=x^2$

for critical points,

$f'(c)=0$

$⇒2x=0$

$⇒x=0$

Now,

$f''(0)=2>0$

∴ $x=0$ is a local minima.