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Thread: Seeking a two-variable function with specific derivatives

  1. #1
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    Seeking a two-variable function with specific derivatives

    Dear all,

    I am looking a function of two variables, f(x,y), with the following features:
    1. The first derivatives are positive, fx>0, fy>0
    2. The second derivatives are negative, fxx<0, fyy<0
    3. The mixed second derivatives is negative, fxy<0

    I have trouble coming up a function having these features, especially the third one.

    Any help will be highly appreciated.

    Thanks.

    Jack
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  2. #2
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    Re: Seeking a two-variable function with specific derivatives

    Quote Originally Posted by Jack0 View Post
    I am looking a function of two variables, f(x,y), with the following features:
    1. The first derivatives are positive, fx>0, fy>0
    2. The second derivatives are negative, fxx<0, fyy<0
    3. The mixed second derivatives is negative, fxy<0
    What is the domain of the function?
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  3. #3
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    Re: Seeking a two-variable function with specific derivatives

    got it

    ln(x+y)

    thanks
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  4. #4
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    Re: Seeking a two-variable function with specific derivatives

    R+

    sorry about that
    and thanks

    what kind of function do we call it? submodular?
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