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Math Help - completely monotone condition

  1. #1
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    Hoa Kỳ
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    completely monotone condition

    Hi all,
    Can someones suggest or give me some hint to do that.
    Find the condition of a > 0, b > 0 and c>0 so that function: f(x)=e-ax/(1+c e-bx) is completely monotone.
    I found the condition at 1st and 2nd derivative but can't do for all derivative order.
    Thanks,
    Last edited by widapol; October 11th 2012 at 06:38 PM.
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  2. #2
    MHF Contributor
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    Re: completely monotone condition

    Hey widapol.

    Can you show us what you got for the first and second derivatives? If you show that the derivative is always increasing (or decreasing) across the entire interval, then that's all you have to do.
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