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How do you determine the behavior of critical points when you have the Hessian?

  1. Mar 14, 2010 #1
    Hello,
    I have solved for the critical points using the gradient, and I have solved for the Hession, which yields a 2x2 matrix. I have plugged in my critical points into the gradient.

    Now, do I apply the same rules as in linear algebra where I find the determinant and trace to calculate positive definite, negative definite, and indefiinite? I currently add up the diagonal and check the determinant. If they are both positive, then it's a local min, if they are both negative, it's a local max, and a saddle point if none of the above, correct?
     
  2. jcsd
  3. Jul 19, 2010 #2
    if fxxfyy-fxy^2 < 0, saddle point

    if fxxfyy-fxy^2 > 0 then

    local maximum if fxx,fyy < 0 and local minimum if fxx,fyy > 0
     
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