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Math Help - function properties

  1. #1
    Newbie
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    Dec 2009
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    Smile function properties

    Hello,

    I've the following function :


    f(x)=((1+(1-2*x/c)^0.5)*exp(-2*x/(1+(1-2*x/c)^0.5))-
    -(1-(1-2*x/c)^0.5)*exp(-2*x/(1-(1-2*x/c)^0.5)))/(1-2*x/c)^0.5

    where 1<x<c/2, c is a positive constant.

    I've to show that f(1)>=x*f(x)

    Any ideas ?

    Asak
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  2. #2
    Grand Panjandrum
    Joined
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    someplace
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    Quote Originally Posted by Asak View Post
    Hello,

    I've the following function :


    f(x)=((1+(1-2*x/c)^0.5)*exp(-2*x/(1+(1-2*x/c)^0.5))-
    -(1-(1-2*x/c)^0.5)*exp(-2*x/(1-(1-2*x/c)^0.5)))/(1-2*x/c)^0.5

    where 1<x<c/2, c is a positive constant.

    I've to show that f(1)>=x*f(x)

    Any ideas ?

    Asak
    Put g(x)=xf(x), and show that x=1 gives a global maximum of g(x).

    CB
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  3. #3
    Newbie
    Joined
    Dec 2009
    Posts
    2
    Hi,

    I've tried to do that, but the derivative is a horror and I can't show that
    g(x)=xf(x) is a decreasing function

    Asak
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