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Question Number 18574 by Tinkutara last updated on 25/Jul/17

The maximum value of f(x) = 2 − ∣x∣^2   − 2x is equal to  (1) 6  (2) 4  (3) 5  (4) 3

$$\mathrm{The}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{of}\:{f}\left({x}\right)\:=\:\mathrm{2}\:−\:\mid{x}\mid^{\mathrm{2}} \\ $$$$−\:\mathrm{2}{x}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{6} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{4} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{5} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{3} \\ $$

Answered by prakash jain last updated on 25/Jul/17

∣x∣^2 =x^2   2−x^2 −2x  =3−x^2 −2x−1  =3−(x+1)^2   (x+1)^2 ≥0  max value=3

$$\mid{x}\mid^{\mathrm{2}} ={x}^{\mathrm{2}} \\ $$$$\mathrm{2}−{x}^{\mathrm{2}} −\mathrm{2}{x} \\ $$$$=\mathrm{3}−{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1} \\ $$$$=\mathrm{3}−\left({x}+\mathrm{1}\right)^{\mathrm{2}} \\ $$$$\left({x}+\mathrm{1}\right)^{\mathrm{2}} \geqslant\mathrm{0} \\ $$$${max}\:{value}=\mathrm{3} \\ $$$$ \\ $$

Commented by Tinkutara last updated on 25/Jul/17

Thanks Sir!

$$\mathrm{Thanks}\:\mathrm{Sir}! \\ $$

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