$f\left(x\right) = x{\left(\log x\right)}^2$ then f is stationary at

$$\begin{gathered} \mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}{\left(\mathrm{logx}\right)}^2 \\ {\mathrm{f}}^{\mathrm{I}}\left(\mathrm{x}\right)=\left(1\right){\left(\mathrm{logx}\right)}^2+\mathrm{x}*2\mathrm{logx}*1/\mathrm{x} \\ =\log \left(\mathrm{x}\right)\left(\mathrm{logx}+2\right) \end{gathered}$$

$\mathrm{f}\left(\mathrm{x}\right)$ is minimum or maximum

$$\begin{gathered} \Rightarrow {\mathrm{f}}^1\left(\mathrm{x}\right)=0 \\ \mathrm{logx}=0 \mathrm{logx}=-2 \\ \mathrm{x}=1 \mathrm{x}={\mathrm{e}}^{-2}=1/{\mathrm{e}}^2 \end{gathered}$$