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Quick Question about Critical Points

  1. Nov 27, 2004 #1

    AKG

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    Say I have a function defined on all of [itex]\mathbb{R}^2[/itex] which is continuous everywhere, and of class [itex]C^{\infty}[/itex]. To find the critical points, I simply find the points where the Jacobian is zero, right (since every point in the domain is in the interior of the domain). Then, to classify the critical points, I look at the eigenvalues of the Hessian (2 x 2)-matrix. If the Hessian has only nonzero eigenvalues, one of which is positive, and one of which is negative at some point c where the Jacobian is zero, then at c, the function has a saddle-point of type (1,1). Is that correct?
     
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