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Finding Negative Definite 'hood

  1. Feb 14, 2009 #1
    Hi,

    I've got a function that I'm trying to show is positively invarient.

    [tex] Let \ V(x,y) = 0.45x^{2}+xy+0.56y^{2} > 0 \ for \ all \ x,y \ in \ R^{2} [/tex]

    [tex] V'(x,y) = ... = -8.4840x^{2} - 18.7412x - 10.3496 - 0.011xy - 0.011y^{2}; [/tex]

    How can I find a neighborhood/region that makes V'(x,y)< 0?
     
  2. jcsd
  3. Feb 15, 2009 #2

    tiny-tim

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    Hi Somefantastik! :smile:

    Complete the square (twice) … write it in the form -A(x - B)2 - C(x - D)2 +E :wink:
     
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