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Critical points and 2nd partials test

  1. Apr 3, 2009 #1
    1. The problem statement, all variables and given/known data

    Find all critical points of f(x,y) = 12xy-x^2 y-2xy^2 and test them for relative extrema using the 2nd partials test.

    2. Relevant equations



    3. The attempt at a solution

    {0=fx(x,y)=12-2x-2 10x-2 x=5
    {0=fy(x,y)=12-4y y=3

    Critical point: (5,3)

    fxx(x,y)= -2
    fyy(x,y)= -4
    fxy(x,y)= 0

    d(5,3)=fxx(5,3)fyy(5,3)-(fxy(5,3))^2
    d=(0)(0)-(0)
    d=0 no conclusion
    ---------------------------------------

    Just wondering if I did this right?
     
  2. jcsd
  3. Apr 3, 2009 #2

    HallsofIvy

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    Science Advisor

    fxx(5,3)fyy(5,3)= (-2)(-4), not (0)(0)!
     
  4. Apr 3, 2009 #3
    Ok, so

    d=(-2)(-4)-(0)
    d=8

    Is that right?
     
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