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Thread: saddle points

  1. #1
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    saddle points



    thank you
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  2. #2
    Senior Member tukeywilliams's Avatar
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    Remember that $\displaystyle D = \det \begin{bmatrix} f_{xx}&f_{xy} \\ f_{yx}&f_{yy} \end{bmatrix} $.

    If $\displaystyle D > 0, \ f_{xx} > 0 $ then we have a minimum. If $\displaystyle D > 0, \ f_{xx} < 0 $ then we have a maximum. If $\displaystyle D < 0 $ then we have a saddle point.
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  3. #3
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    still a bit confused by this
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  4. #4
    Senior Member tukeywilliams's Avatar
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    $\displaystyle f_x = 3x^2-3y = 0 $
    $\displaystyle f_y = -3y^2-3x = 0 $

    Now solve for $\displaystyle (x,y) $ such that the above holds. $\displaystyle (0,0) $ is a critical point. $\displaystyle (-1,1) $ is also CP.
    Last edited by tukeywilliams; Dec 3rd 2007 at 02:41 AM.
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  5. #5
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    would you be able tos how me a step by step on how to get from question to the answer so I no for future questions please?
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