The area (in sq.

Question

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 :

Accepted Answer

Area (A) = 2t. (1$-$t2)

(0 < t < 1)

A = 2t $-$ 2t3

$${{dA} \over {dt}} = 2 - 6{t^2}$$ = 0

$$ \Rightarrow $$ $t =$ $ \pm $$ ${1 \over {\sqrt 3 }}$$

$$ \therefore $$ $$ {A_{\max }} = |{2 \over {\sqrt 3 }}\left( {1 - {1 \over 3}} \right)| = {4 \over {3\sqrt 3 }}$$

Solutions · 1