Q. Find the area (in sq. units) of the largest rectangle with lower base on the x-axis \& upper vertices on thecurve $\mathrm{y}=12-\mathrm{x}^{2}$.
Application of Derivatives
Solution:
$ A=2 x y $
$f^{\prime}(x)=A(2 x)\left(12-x^2\right)$
$f^{\prime}(x)=2\left[12-3 x^2\right] $
$ x=2 $
$f^{\prime \prime}(x)=2[-6]=\max$
$y=12-4=8$
$\text { Area }=2 \times 8 \times 2=32 \text { sq. units }$
