Results 1 to 2 of 2

Math Help - Advanced Calc (Properties of Continuous Functions)

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    38

    Advanced Calc (Properties of Continuous Functions)

    Suppose that f: [a, b][a,b] is continuous. Prove that there is at least one fixed point in[a, b] - that is, x such that f(x)=x.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by lacy1104 View Post
    Suppose that f: [a, b][a,b] is continuous. Prove that there is at least one fixed point in[a, b] - that is, x such that f(x)=x.
    Hint: Define g(x) = f(x) - x. Now use intermediate value theorem to show g has a zero on [a,b].
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 11th 2010, 07:18 PM
  2. More Properties of Continuous Functions
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: May 6th 2009, 10:22 PM
  3. Properties of Continuous Functions
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: May 5th 2009, 04:01 PM
  4. properties of continuous functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 23rd 2009, 03:37 PM
  5. advanced functions intro calc questions
    Posted in the Calculus Forum
    Replies: 4
    Last Post: February 23rd 2009, 10:00 AM

Search Tags


/mathhelpforum @mathhelpforum