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Question Number 167278 by mnjuly1970 last updated on 11/Mar/22

Answered by mr W last updated on 11/Mar/22

$$f\left(x\right)=\frac{\sqrt{x(x^2+1)}}{x^2+1+x}=\frac{1}{\sqrt{\frac{x^2+1}{x}}+\sqrt{\frac{x}{x^2+1}}}$$$$=\frac{1}{\sqrt{x+\frac{1}{x}}+\frac{1}{\sqrt{x+\frac{1}{x}}}}$$$$⩽\frac{1}{\sqrt{2}+\frac{1}{\sqrt{2}}}=\frac{\sqrt{2}}{3}=f_{max}$$

Commented by mnjuly1970 last updated on 12/Mar/22

$$thanksalotSirW$$

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