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Math Help - Need help with ln and e stuff

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    Need help with ln and e stuff

    I need help with a question. It says:
    Graph and state all important points and intervals: y=(lnx)/(x)
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    Quote Originally Posted by CenturionMonkey View Post
    I need help with a question. It says:
    Graph and state all important points and intervals: y=(lnx)/(x)
    Well lets start by taking the derivative

    \frac{dy}{dx}=\frac{x \cdot \frac{1}{x}-(1) \cdot \ln(x)}{x^2}=\frac{1-\ln(x)}{x^2}

    So our critical numbers are the zero's of the derivative

     1 -\ln(x)=0 \iff 1 =\ln(x) \iff e=x

    The inflection points are given by the 2nd derivative

    \frac{d^2y}{dx^2}=\frac{x^2 \cdot\frac{-1}{x}-(2x)(1-\ln(x)}{x^4}=\frac{-3x+\ln(x)}{x^4}

    setting equal to zero we get

     -3x+\ln(x)=0

    This has no Real solutions see graphs below

    So the graph will look like the next one

    Good luck
    Attached Thumbnails Attached Thumbnails Need help with ln and e stuff-solu.jpg   Need help with ln and e stuff-ln.jpg  
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