Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be given by $f(x)=\left|x^2-1\right|$, then

• A

  $f$ has a local minima at $x= \pm 1$ but no local maxima
• B

  $f$ has a local maxima at $x=0$, but no local minima
• Correct answer
  C

  f has a local minima at $x= \pm 1$ and a local maxima at $x=0$
• D

  f has neither any local maxima nor any local minima

Solution

By figure, $f$ has a local minima at $x= \pm 1$ and a local maxima at $x=0$

Hence, the correct answer is option: 'C'.