Mathematics - Application of Derivative Question with Solution | TestHub

Let the rectangle is (ABCD)

$\begin{array}{rl}& A=(t,0),B=\left(t,e^{-t}\right),C=\left(-t,e^{-t}\right),D=(-t,0)\\ & ABCD=2t{e}^{-t}=f(t)\\ & \frac{df}{dt}=2\left(t\left(-e^{-t}\right)+e^{-t}\right)=2e^{-t}(1-t)\\ & \frac{df}{dt}>0\Rightarrow t\in (0,1)\\ & \frac{df}{dt}<0\Rightarrow t\in (1,\infty )\\ & t=1\text{ is point of maxima }\\ & \text{ max area }=f(1)=\frac{2}{e}\end{array}$