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

• A

  f has a local minimum at $x=\pm 1$ but no local maximum
• B

  f has a local maximum at $x=0$ but no local minimum
• Correct answer
  C

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

  f has neither a local maxima nor a local minima at any point

Solution

$f$ has a local minima at $x=\pm 1$ and local maximum at $x=0$

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