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Min max using partial derivatives

  1. Oct 27, 2008 #1
    (x^2 + y^2)*e^(y^2 - x^2)
    I am having trouble finding the critical points.

    Fx=2xe^(y^2-x^2)(1-x^2-y^2)=0
    Fy=2ye^(y^2 - x^2)(1+x^2 +y^2)=0

    or
    0=x(1-x^2-y^2)
    0=y(1+x^2+y^2)

    now, finding all the roots is giving me trouble. x and y obviously = 0, but I am unsure how to move forward to get the rest of the zeros, therefore giving me the critical points. Any help would be appreciated. Thanks.

    Stephen
     
  2. jcsd
  3. Oct 28, 2008 #2

    Mark44

    Staff: Mentor

    Fx = 0 iff x = 0 or x^2 + y^2 = 1
    That is, Fx = 0 when x = 0 or when (x, y) is a point on the unit circle centered at (0, 0).

    Fy = 0 iff y = 0 (1 + x^2 + y^2 >= 1 for all real (x, y) )
    So both partials are 0 simultaneously for (0, 0), (1, 0), or (-1, 0).
     
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