Using calculus and technology, sketch the graph of f(x)=xe^x.Be sure to note any relative and/or absolute extrema, point(s) of inflection and any asymptotic features. Show all symbolic work that helps you arrive at your conclusions.
Use the product rule:
Let $\displaystyle f = x $ and $\displaystyle g = e^x$
$\displaystyle (f ')(g) + (f) (g ')$
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$\displaystyle f(x) = xe^x$
$\displaystyle f '(x) = (1)(e^x) + (x)(e^x)$
$\displaystyle f "(x) = e^x + \left[(1)(e^x) + (x)(e^x)\right]$
Then simplify. If you are not comfortable using the product rule, you need to practice. It will be something you frequently use in calculus.