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Thread: Graph of a function

  1. #1
    Junior Member
    Feb 2009

    Post Graph of a function

    List all the asymptotes of the graph of the function and the approximate coordinates of each local extremum.


    I've had a hard time trying to solve this graph , I used my graphing calculator, but it didn't help me.
    Acording to my book, the negative x axis is an asymptote. Can someone explain me how to interpret and graph the function properly? Thanks in advance!
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  2. #2
    MHF Contributor
    Nov 2008

    f(x) = x\:2^x = x\:e^{2\ln x}

    f'(x) = e^{2\ln x} (1 + x \ln 2)

    Therefore f is decreasing from -\infty to -\frac{1}{\ln 2} and increasing from -\frac{1}{\ln 2} to +\infty

    The minimum has coordinates (-\frac{1}{\ln 2} ; -\frac{1}{e\:\ln 2})

    The limit in -\infty is 0 which shows that x-axis is an asymptot

    The limit in +\infty is +\infty

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