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Math Help - Max/Min with constraint

  1. #1
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    Max/Min with constraint

    I need help on the following problem:

    Find the absolute maximum and minimum of the function  f(x,y) = x^2 + y^2 subject to the constraint  x^4 + y^4 = 625 .

    I tried using Lagrange's multiplier to this problem but here is where I'm stuck.

     \frac{\partial f}{\partial x}= \lambda\frac{\partial g}{\partial x}

     2x = 4x^3 \lambda

    \frac{\partial f}{\partial y} = \lambda\frac{\partial g}{\partial y}

    2y = 4y^3\lambda

    I just can't seem to be able to solve for  x,y, \lambda ,which I need for the critical points
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  2. #2
    MHF Contributor
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    Where is your third equation?

    2x\;=\;4x^{3}\lambda

    2y\;=\;4y^{3}\lambda

    x^{4}\;+\;y^{4}\;=\;625

    That should do it.
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