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Math Help - Derivatives

  1. #1
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    Derivatives

    Problem
    Given f\left( x,y \right)=e^{2x^{2}+4xy^{2}-x},
    find and classify the extremes.


    Attempt
    I have a problem with the second derivatives. That expression would be huge. Have I been thinking wrong? Here's my calculations:
    * 2012-09-07 15.15.06.jpg
    * 2012-09-07 15.15.15.jpg
    * 2012-09-07 15.15.21.jpg


    The method I use to classify is:
    When A\mbox{C}-B^{2} is positive, we have a min or maximum. If A>0 then it's a min, if A<0 it's a maximum. If A\mbox{C}-B^{2} is negative, then we have a saddle point.
    \left(A=\frac{\partial ^{2}}{\partial x^{2}},\; B=\frac{\partial ^{2}}{\partial xy},\; \mbox{C}=\frac{\partial ^{2}}{\partial y^{2}} \right)
    Last edited by jacob93; September 10th 2012 at 11:38 AM.
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  2. #2
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    Re: Derivatives

    You're doing it correctly, including the classification. You just need to keep going. For A, where you stopped for some reason, plug f and df/dx in and you're done. (Actually, you don't even need to do that much work, since you're evaluating it at 3 points (0,.5), (0,-.5), (.25,0) where you already know df/dx=0. Thus A(P)=4f(P) when P is one of those 3 points.)
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  3. #3
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    Re: Derivatives

    The second derivatives are NOT 'huge'. They are not a problem if you are careful.
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  4. #4
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    Re: Derivatives

    thanks
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