Question Number 202298 by hardmath last updated on 24/Dec/23
$$\mathrm{x}\:\in\:\mathbb{R} \\ $$$$\mathrm{Find}:\:\:\:\boldsymbol{\mathrm{max}}\left(\frac{\mathrm{5}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{6x}\:+\:\mathrm{11}}\right)\:=\:? \\ $$
Answered by Rasheed.Sindhi last updated on 24/Dec/23
$$\boldsymbol{\mathrm{max}}\left(\frac{\mathrm{5}}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{6x}\:+\:\mathrm{11}}\right)=\boldsymbol{\mathrm{max}}\left(\frac{\mathrm{5}}{\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{2}}\right) \\ $$$$=\frac{\mathrm{5}}{\boldsymbol{\mathrm{min}}\left(\:\left({x}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{2}\:\right)}=\frac{\mathrm{5}}{\left(\mathrm{3}−\mathrm{3}\right)^{\mathrm{2}} +\mathrm{2}}=\frac{\mathrm{5}}{\mathrm{2}} \\ $$$${at}\:{x}=\mathrm{3} \\ $$