JEE PYQ: Application Of Derivatives Question 35
Question 35 - 2020 (04 Sep Shift 2)
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 $y = x^2 - 1$ below the $x$-axis, is:
(1) $\frac{2}{3\sqrt{3}}$
(2) $\frac{1}{3\sqrt{3}}$
(3) $\frac{4}{3}$
(4) $\frac{4}{3\sqrt{3}}$
Show Answer
Answer: (4)
Solution
Area $= 2x(x^2 - 1)$ for $0 < x < 1$ (below axis, area is $2x(1 - x^2)$). Maximize: $\frac{dA}{dx} = 2 - 6x^2 = 0 \Rightarrow x = \frac{1}{\sqrt{3}}$. Max area $= \frac{4}{3\sqrt{3}}$.
BETA
