Math Help - Help finding relative & absolute extrema, points of inflection & asymptotic features.

1. Help finding relative & absolute extrema, points of inflection & asymptotic features.

This is brand new material as of yesterday so I need a little help figuring it out. I am told to graph f(x) and note any relative and/or absolute extrema, point(s) of inflection and any asymptotic features.

f(x) = xe^x

Thanks in advance for any insight.

2. The answers depend on the first and second derivatives of $f(x)$:

\begin{aligned}
f(x)&=xe^x\\
f'(x)&=1\cdot e^x+x\cdot e^x=xe^x+e^x\\
f''(x)&=\frac{d}{dx}\left(xe^x\right)+\frac{d}{dx} \left(e^x\right)=xe^x+2e^x.
\end{aligned}