R D Sharma Solutions for Chapter: Maxima and Minima, Exercise 1: EXERCISE

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

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

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

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

Find the local extremum values of the function $\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{x}-1\right){\left(\mathrm{x}-2\right)}^2$

 Find the local extremum values of the function $\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}\sqrt{1-\mathrm{x}.}$

Find the local extremum values of the $\mathrm{f}\left(\mathrm{x}\right)=-{\left(\mathrm{x}-1\right)}^3{\left(\mathrm{x}+1\right)}^2$.