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Question Number 207712 by efronzo1 last updated on 24/May/24

Answered by Frix last updated on 24/May/24

$$\mathrm{For}x=q\mathrm{and}A=\left(\begin{array}{c}p\\ 0\end{array}\right)\mathrm{the}\mathrm{area}\mathrm{is}(q-p)\sqrt{p}$$$$\frac{d\left[(q-p)\sqrt{p}\right]}{dp}=0$$$$\frac{q-3p}{2\sqrt{p}}=0\Rightarrow p=\frac{q}{3}$$$$\mathrm{Max}\mathrm{area}=\frac{2\sqrt{3}{q}^{\frac{3}{2}}}{9}$$$$q=4\Rightarrow \mathrm{answer}\mathrm{is}\frac{16\sqrt{3}}{9}$$

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