Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Does the critical value exist?

  1. Aug 24, 2004 #1


    User Avatar

    There is a problem in Arnold's Trivia :yuck::
    Find the critical values and critical points of the mapping z -> z^2+ 2*conjugate(z); (sketch the answer).
    It seems to me that the critical values (z where f'(z)=0) do not exist, becouse the function f(z)= z^2+ 2*conjugate(z) is not analytic.
    Is anybody able to explain what Arnold mean under the notion 'critical values and critical points'?

    Thanx for help.
  2. jcsd
  3. Aug 25, 2004 #2
    if i'm not mistaken, a critical value would also be a place where f' is undefined (in addition to a point where f' is zero).

    you can use the cauchy riemann equations but i think you have to see if the function is analytic at the origin using the limit definiton of derivative though i'm not sure.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Does the critical value exist?
  1. Does 0.999 exist? (Replies: 2)