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

  1. #1
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    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.
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  2. #2
    Senior Member
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    The answers depend on the first and second derivatives of f(x):

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