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Math Help - stationary points(an unholy mess)

  1. #1
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    stationary points(an unholy mess)

    Determine the stationary points of the function

    f(x,y)=(x^2+(1/2)xy+y^2)e^(x+y)

    after differentiating i get

    df/dx = x^2 + 2x +(1/2)xy + (1/2)y +y^2 = 0 ...eq1

    and

    df/dy = y^2 + (1/2)x +(1/2)xy + 2y +y^2 = 0 ...eq2

    i then solved these 2 eqs simultanously and got

    y= (-4/3)x^2 - x

    which i subed back into eq 1 which turnrf into a unholy mess
    can anyone please help me...where am i going wrong?
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  2. #2
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    Quote Originally Posted by fitzgilbert View Post
    Determine the stationary points of the function

    f(x,y)=(x^2+(1/2)xy+y^2)e^(x+y)

    after differentiating i get

    df/dx = x^2 + 2x +(1/2)xy + (1/2)y +y^2 = 0 ...eq1

    and

    df/dy = y^2 + (1/2)x +(1/2)xy + 2y + y^2 = 0 ...eq2 Mr F says: This is wrong. The term in red should be x^2. Is it a typo or were you using it when attempting the calculations?

    i then solved these 2 eqs simultanously and got

    y= (-4/3)x^2 - x

    which i subed back into eq 1 which turnrf into a unholy mess
    can anyone please help me...where am i going wrong?
    By the way, in case you didn't realise .....

    Since f(x, y) is symmetric in x and y you can easily get \frac{\partial f}{\partial y} simply by swapping the x's and y's around in your expression for \frac{\partial f}{\partial x}. No need to waste time partial differentiating again ......
    Last edited by mr fantastic; February 7th 2008 at 03:31 PM.
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