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Thread: Find all inflection points

  1. #1
    Apr 2009

    Find all inflection points

    I know to find inflection points you need to compute the 2nd derivative test and set equal to 0. I think I got the 2nd derivative but I'm lost on the rest. Here is the problem with 1st and 2nd derivatives computed:

    Problem #1 -

    f(x) = e^(-x^2/2) / sqrt[2*pi]

    f'(x) = -e^(-x^2/2) / sqrt[2*pi]

    f"(x) = e^(-x^2/2) (x^2-1) / sqrt[2*pi]

    I have another problem to find inflection pts. No idea where to start:

    Problem #2 -

    g(x) = e^[(-(x-a)^2)/(2b^2)] / sqrt[2*pi*b^2]

    Can anyone help?? These are tough problems!!
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  2. #2
    Eater of Worlds
    galactus's Avatar
    Jul 2006
    Chaneysville, PA
    It is easier to solve the 2nd derivative than you may think at first glance.

    $\displaystyle \frac{(x^{2}-1)e^{\frac{-x^{2}}{2}}}{\sqrt{2\pi}}=0$

    Concentrate on the numerator. e is never 0, so all we have to do is solve

    $\displaystyle x^{2}-1=0$, x=1, x=-1
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