Find the point of local maxima or local minima and corresponding local maximum and local minimum values of $\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{x}-1\right){\left(\mathrm{x}+2\right)}^2$. Also, find the points of inflection.

Find the point of local maxima or local minima and corresponding local maximum and local minimum values of $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}+\frac{{\mathrm{a}}^2}{\mathrm{x}},\mathrm{a}>0,\mathrm{x}\ne 0$. Also, find the points of inflection, if any.