Results 1 to 3 of 3

Math Help - Implicit Function Theorem

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    2

    Implicit Function Theorem

    (i) Let be a smooth 1-parameter family of functions on , with . Use the implicit function theorem to show there are neighbourhoods and of 0 such that for each the function has a unique critical point in .
    (ii) Consider the family . Show that for has more than one critical point. Explain briefly why this does not contradict the statement in part (i) of this question.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Why not type your own question.
    Learn to use LaTeX.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    2
    sorry, but I thought it would be quicker to just post it, as it does not involve much complex notation
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Implicit Function Theorem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 3rd 2011, 10:16 AM
  2. Implicit Function Theorem for f(x1,...,xm, y1,...,yn) = 0
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 9th 2011, 06:45 AM
  3. Implicit Function Theorem
    Posted in the Calculus Forum
    Replies: 6
    Last Post: October 15th 2010, 05:24 PM
  4. Replies: 0
    Last Post: November 13th 2009, 05:41 AM
  5. Replies: 0
    Last Post: October 19th 2009, 07:58 PM

Search Tags


/mathhelpforum @mathhelpforum