Question Number 18574 by Tinkutara last updated on 25/Jul/17
$$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\mathrm{2}\:−\:\mid{x}\mid^{\mathrm{2}} \\ $$$$−\:\mathrm{2}{x}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{5} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{3} \\ $$
Answered by prakash jain last updated on 25/Jul/17
$$\mid{x}\mid^{\mathrm{2}} ={x}^{\mathrm{2}} \\ $$$$\mathrm{2}−{x}^{\mathrm{2}} −\mathrm{2}{x} \\ $$$$=\mathrm{3}−{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1} \\ $$$$=\mathrm{3}−\left({x}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\left({x}+\mathrm{1}\right)^{\mathrm{2}} \geqslant\mathrm{0} \\ $$$${max}\:{value}=\mathrm{3} \\ $$$$ \\ $$
Commented by Tinkutara last updated on 25/Jul/17
$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$