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Math Help - Classifying critical points

  1. #1
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    Classifying critical points

    Hello

    Im trying to find all the critical points of this functions.

    Could somebody please give me a hand?

    Thanks Heaps
    Attached Thumbnails Attached Thumbnails Classifying critical points-q2ac.bmp  
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  2. #2
    Moo
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    Hello,

    f(x,y)=x^2+x^2y+5y^2+2y^3

    \frac{\partial f}{\partial x} (x,y)=2x+2xy=2x(1+y)

    \frac{\partial f}{\partial y} (x,y)=x^2+10y+6y^2

    You have to solve simultaneously these equations :

    \left\{ \begin{array}{ll} 0&=2x(1+y) \\ 0&=x^2+10y+6y^2 \end{array} \right.

    from the first equation, you know that either x=0, either y=-1.
    Then substitute in the second equation, for each possible value.

    Then, calculate the Hessian matrix, and here, I don't know how much you've learnt :/
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  3. #3
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    Confused?

    Hey

    sorry to bother you, but i solved the two equations simultaneously and now im not exactly sure what i need to do? Could you show your working so i can get a clear and definite way to solve this type of problem.

    Thank you
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  4. #4
    Moo
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    Sorry, I didn't see your answer...

    Take a look at this link : Hessian matrix - Wikipedia, the free encyclopedia
    Normally, everything is explained (Note that you have to take the values of the second derivatives at the critical points).

    I don't feel like typing all the tex, but I can do it by hand if you really need it
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