For $y=xe^{-x}$, find $\frac{\mathrm d^2y}{\mathrm dx^2}$. Determine the value of $x$ for whic

Question

For $y=xe^{-x}$, find $\frac{\mathrm d^2y}{\mathrm dx^2}$. Determine the value of $x$ for which this second derivative is zero.

Accepted Answer

$\frac{\mathrm d^2y}{\mathrm dx^2}=e^{-x}(x-2);\ x=2$

Second derivative of an exponential product