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Math Help - Help with max/min with 2 variables

  1. #1
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    Help with max/min with 2 variables

    f = x^4 + y^4 - 4xy

    I know how to find the critical points and test whether they are local min or max. However, for the function above, I found many critical points that could all be classified as local minimum.

    The answer only gives two of those points as local minimum.

    Can anyone suggest what I do after i find many critical points that could all be local minimum?
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  2. #2
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    Just one question:
    how was the function given: like f(x) = ;or y= ;or like what you posted?
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  3. #3
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    the function was given as f(x,y) =
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  4. #4
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    Quote Originally Posted by messianic View Post
    f = x^4 + y^4 - 4xy

    I know how to find the critical points and test whether they are local min or max. However, for the function above, I found many critical points that could all be classified as local minimum.

    The answer only gives two of those points as local minimum.

    Can anyone suggest what I do after i find many critical points that could all be local minimum?
    There are three critical points, found by solving x^3 - y = 0 and y^3 - x = 0 simultaneously:

    (0, 0), (1, 1) and (-1, -1).

    Their nature is tested in the usual way.

    If you need more help, please post all your work and say where you're stuck.
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