If $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^5-5{\mathrm{x}}^4+5{\mathrm{x}}^3-10$ has local maximum and minimum at $\mathrm{x}=\mathrm{p}\text{ and }\mathrm{x}=\mathrm{q}$, respectively, then $(\mathrm{p},\mathrm{q})\equiv$

$\frac{\mathrm{dy}}{\mathrm{dx}}=5{\mathrm{x}}^2(\mathrm{x}-1)(\mathrm{x}-3)=0$
$\therefore \mathrm{x}=0,1,3$

Clearly, $x=0$ is neither a point of maxima nor a point of minima as derivative does not change sign at $x=0$. 
$x=1$ is a point of maxima and $x=3$ is a point of minima.