1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fixed points and graphs

  1. Mar 27, 2006 #1
    Hi, I was thinking about the following and would like some clarification. Suppose that we have a continuous scalar function [itex]f:R^n \to R[/itex] with a critical point at say x_0, where the dimension of x_0 depends on the value of n.

    Consider as an example f(x) = x (n = 1). The point x = 0 is a critical point since f'(x) is zero at that point. Since f is continuous then corresponding to x = 0 must be a local minimum, local maximum or saddle correct? (Not exactly sure about it)

    My point is that x = 0 lies on a line of fixed points and hence cannot correspond to a maximum or a minimum? Is this true in higher dimensions or does this reasoning hold at all?

    Any help would be good thanks.
  2. jcsd
  3. Mar 27, 2006 #2
    if f(x) = x, then f'(x) = 1 for all x. so x=0 is not a critical point. f is an increasing function.
    Last edited: Mar 27, 2006
  4. Mar 27, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor

    As nocturnal said, if f(x)= x then x= 0 is NOT a critical point. Maybe you were thinking of f'(x)= x which would correspond to f(x)= (1/2)x2+ C. That really does have a minimum at x= 0.
  5. Mar 29, 2006 #4
    Oops, I should watch my differentiation...better hope that doesn't happen during an exam.:biggrin:
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Fixed points and graphs
  1. Fixed point equation (Replies: 2)

  2. Fixed Point Problems (Replies: 3)