Question

Find the critical points of the following function and test them for their maxima and minima.
$y=x\cdot e^x$

Answer 1

$y=x.e^x$

$\frac{dy}{dx}=e^x+x{e}^x=0\Rightarrow x=-1$

$\frac{d^{2}y}{d{x}^2}=2e^x+x{e}^x$

For $x=-1,\frac{d^{2}y}{d{x}^2}>0$,Hence it has minimum at $x=-1$ and increases continously in $(-1,\infty )$