JEE MAIN - Mathematics (2020 - 4th September Evening Slot - No. 3)
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 parabola, y = x2–1 below the x-axis, is :
$${1 \over {3\sqrt 3 }}$$
$${2 \over {3\sqrt 3 }}$$
$${4 \over {3\sqrt 3 }}$$
$${4 \over 3}$$
Explanation
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Area (A) = 2t. (1$$ - $$t2)
(0 < t < 1)
A = 2t $$ - $$ 2t3
$${{dA} \over {dt}} = 2 - 6{t^2}$$ = 0
$$ \Rightarrow $$ $$t = $$$$ \pm $$$${1 \over {\sqrt 3 }}$$
$$ \therefore $$ $$ {A_{\max }} = |{2 \over {\sqrt 3 }}\left( {1 - {1 \over 3}} \right)| = {4 \over {3\sqrt 3 }}$$
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