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Question Number 62211 by Tony Lin last updated on 18/Jun/19

$$\frac{x}{\sqrt{4-x^2}+3}Max=\frac{5}{3}?$$

Commented by MJS last updated on 17/Jun/19

$$\mathrm{what}\mathrm{does}\mathrm{this}\mathrm{mean}?$$

Commented by Tony Lin last updated on 17/Jun/19

$$howtofindthemaximumvalueof$$$$\frac{x}{\sqrt{4+x^2}-3}?$$

Commented by MJS last updated on 18/Jun/19

$$f\left(x\right)=\frac{x}{\sqrt{4-x^2}+3}\mathrm{is}\mathrm{defined}\mathrm{for}x\in [-2;2]$$$$\mathrm{the}\mathrm{derivate}\mathrm{is}\mathrm{not}\mathrm{defined}\mathrm{for}\mathrm{the}\mathrm{borders}$$$$\Rightarrow \mathrm{if}{\mathrm{there}}^{\prime }\mathrm{s}\mathrm{no}\mathrm{other}\mathrm{minimum}\mathrm{or}\mathrm{maximum}$$$$\mathrm{look}\mathrm{at}\mathrm{these}\mathrm{borders}$$$$f\left(2\right)=\frac{2}{3}\mathrm{is}\mathrm{the}\mathrm{maximum}$$$$\mathrm{because}$$$$f^{\prime }\left(x\right)=\frac{4+3\sqrt{4-x^2}}{(3+\sqrt{4-x^2})\sqrt{4-x^2}}>0\mathrm{\forall }x\in ]-2;2[$$

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