Which one of the following is correct in respect of the function...

$f(x)=x(x-1)(x+1)=x$\left(x^2-1\right)$Differentiating, we get$f^{\prime}(x)=x(2 x)+\left(x^2-1\right)=2 x^2+x^2-1=3 x^2-1$Again differentiating$f^{\prime \prime}(x)=6 x \operatorname{At}^{\prime}(x)=0 \Rightarrow 3 x^2-1=0 \Rightarrow x^2=\frac{1}{3} \Rightarrow x= \pm \frac{1}{\sqrt{3}}$Maximum value of$f(x)=f\left(\frac{-1}{\sqrt{3}}\right)=\frac{-1}{\sqrt{3}}\left(\left(\frac{-1}{\sqrt{3}}\right)^2-1\right)$=\frac{-1}{\sqrt{3}}\left(\frac{1}{3}-1\right)=\frac{-1}{\sqrt{3}}\left(\frac{-2}{3}\right)=\frac{2}{3 \sqrt{3}}$ Minimum value of $f(x)=f\left(\frac{1}{\sqrt{3}}\right)=\frac{1}{\sqrt{3}}\left(\frac{1}{3}-1\right)=\frac{-2}{3 \sqrt{3}}$