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!

Can a function have a local max but no global max?

  1. Nov 17, 2014 #1
    1. The problem statement, all variables and given/known data
    I need to confirm if I correct in saying the following:
    If f(x) is a function having the domain [a,b) as shown in the figure, then f(x) has several local maxima but none of them is global maximum, and f(x) does not have a global maximum.
    H3dG3Jm.png

    2. Relevant equations and definitions
    Global Maximum: f(c) is said to be the global maximum of a function f(x) if f(c)≥f(x) for all x on the domain of f(x).

    3. The attempt at a solution
    There exists no point c in the domain of f(x) such that f(c)≥f(x) for all x in the domain. Hence, although f(x) has several local maxima, f(x) does not have a global maximum.
     
  2. jcsd
  3. Nov 17, 2014 #2

    Mark44

    Staff: Mentor

    Yes, the function in this graph has no global maximum.
     
  4. Nov 17, 2014 #3

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper


    You are correct: the function has a (global) supremum, but not a global maximum on [a,b).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Can a function have a local max but no global max?
  1. Local max (Replies: 12)

  2. Global max/min on disc (Replies: 7)

Loading...