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Last part of extreme value problem

  1. Feb 16, 2006 #1
    Hey hey!

    I'm trying to figure out the extreme values of

    f(x,y,z) = (x^2 + y^2 - z^2) * e^-(x^2+y^2+z^2)

    I do partial differentiation to find where all derivatives are zero, and after some work come to the equation

    2(x^2 + y^2 - z^2) = 0

    So one obvious extreme point is (0,0,0), but what about x^2 + y^2 - z^2? I figured it's a extreme value circle of radius 1 in the xy-plane, but what about when z isn't 0? Would really appreciate some pointers guys. Thanks! :!!)
  2. jcsd
  3. Feb 16, 2006 #2


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    Well, the equation there is the equation of a double cone. You have
    x^2 + y^2 = z^2
    and for every value of z this determines a circle with radius z.
    In the xy plane the circle will have radius 0, not 1.
    Last edited: Feb 16, 2006
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