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Simple Multivariable extrema

  1. Feb 9, 2013 #1
    1. The problem statement, all variables and given/known data
    f = x^2 + 4xy + y^2 + 6x + 8
    Find minimum, maximum, or saddle point

    2. Relevant equations
    A = [f_xx, f_xy; f_yx, f_yy]

    3. The attempt at a solution

    Found the determinant to be zero ( i got [2 ,4; 4, 2] ) so i cant use the eigenvalues to determine the extrema.

    now what do i do? If I am to use lagrange multipliers, how do i do that without a constraint?
     
  2. jcsd
  3. Feb 9, 2013 #2

    haruspex

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    Yes, that method breaks down here. Try a change of coordinates to break the symmetry between the second order x and y terms.
     
  4. Feb 9, 2013 #3
    How is the determinant 0?

    EDIT: Sorry, I forgot I can't give out full solutions.

    Make sure you are finding the determinant correctly.
     
    Last edited: Feb 9, 2013
  5. Feb 9, 2013 #4

    haruspex

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    Good point - I failed to check that claim.
     
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