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!

Continuity & Properties of functions

  1. May 7, 2008 #1
    1. The problem statement, all variables and given/known data

    Let f:R->R be a continuous function where limit as x goes to positive/negative infinity is negative infinity. Prove that f has a maximum value on R.

    2. Relevant equations

    3. The attempt at a solution
    I tried to use the definition of infinite limits but I'm not sure how to do this explicitly.
  2. jcsd
  3. May 7, 2008 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Let X be a real number. Since [itex]\lim_{x\rightarrow \infty}= -\infty[/itex], there exist x1[/sup] such that if x> x1, f(x)< X. Since [itex]\lim_{x\rightarrow -\infty}= -\infty[/itex], there exist x2 such that if x< x2, f(x)< X. Now look at the values of f(x) on the closed and bounded interval [x1, x2].
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Continuity & Properties of functions