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Math Help - Intervals on which function is decreasing and increasing

  1. #1
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    Intervals on which function is decreasing and increasing

    Hey, could someone please guide me as to what to do next in this problem. Thanks!

    f(x) = xe-(x^2)/2

    Determine the intervals where f is increasing and where f is decreasing.

    I've worked out the derivative, but am unsure how to proceed.

    Update: I've worked out that the derivative is positive for -1 < x < 1 and negative for x > 1 and x < -1 ... but my working seems quite dodgy, just a bit of guidance would be great. Thanks.
    Last edited by Vishak; May 10th 2013 at 05:23 PM.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Intervals on which function is decreasing and increasing

    You are correct, but how did you determine this...what did you get for the derivative?
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  3. #3
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    Re: Intervals on which function is decreasing and increasing

    I got f'(x) = e(-x^2)/2(1+x)(1-x)

    The I set f'(x) > 0 and solved, and did the same for f'(x) < 0
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Intervals on which function is decreasing and increasing

    I see nothing "dodgy" about that. I would probably write:

    f'(x)=e^{-\frac{x^2}{2}}(1-x^2)

    observe that e^{-\frac{x^2}{2}}>0 for all real x, and then observe:

    1-x^2

    is positive on (-1,1) and negative on (-\infty,-1)\,\cup\,(1.\infty).

    What you did seems find to me.
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