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.

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of each of the following function. Also, find the points of inflection, if any:

$f\left(x\right)=x^4-62x^2+120x+9$

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of the following function. Also, find the points of inflection, if any:

$f\left(x\right)=x^3-6x^2+9x+15$

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of the following function. Also, find the points of inflection, if any:

$f\left(x\right)=(x+1)(x+2{)}^{\frac{1}{3}}, x\ge -2$