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Finding critical points

  1. May 2, 2007 #1
    1. The problem statement, all variables and given/known data
    Explain why f has no absolute maximum or minimum. How about critical points?

    2. Relevant equations
    Hint: it is simplest to make 3 cases: a) x+y+z does not =0 b) x+y+z=0 c) x=y=z=0

    3. The attempt at a solution
    I did cases b and c, but I'm not sure how to go about doing a. Also, I'm not sure how to explain why the function does not have an absolute max or min.
  2. jcsd
  3. May 5, 2007 #2
    Can anyone help?
  4. May 5, 2007 #3
    hmmm, simplifying things,

    how can you bound f(x,y,z) from below? what about from above? can you make f arbitrarily big?
    can you make f(x,y,z) arbitrary close to some values? try some additional cases, suppose x=y=z not equaling zero?

    edit: additional hint: cylindrical coordinate.
    Last edited: May 5, 2007
  5. May 5, 2007 #4
    Thank you!
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