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  • The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the probola,  

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the probola, y = x^{2}-1 below the x-axis is:
Option: 1 \frac{2}{3\sqrt{3}}
Option: 2 \frac{1}{3\sqrt{3}}
Option: 3 \frac{4}{3}
Option: 4 \frac{4}{3\sqrt{3}}

Answers (1)

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\\\text { Area }(\mathrm{A})=2 \mathrm{t} .\left(1-\mathrm{t}^{2}\right) \\ (0<\mathrm{t}<1) \\ \mathrm{A}=2 \mathrm{t}-2 \mathrm{t}^{3} \\ \frac{\mathrm{d} \mathrm{A}}{\mathrm{dt}}=2-6 \mathrm{t}^{2} \\ \mathrm{t}=\frac{1}{\sqrt{3}}

\Rightarrow \mathrm{A}_{\max }=\frac{2}{\sqrt{3}}\left(1-\frac{1}{3}\right)=\frac{4}{3 \sqrt{3}}

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himanshu.meshram

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