1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Analysis homework help

  1. Apr 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Let A= [0,1). Find a continuous function g: from A to R that does not attain a maximum value.

    2. Relevant equations

    3. The attempt at a solution
    I believe that g(x)=x or g(x)=e^x represent such a function, but I do not know how to use the IVT to prove that either of them work. Please help! I need as much information as possible without completely giving away the answer.
  2. jcsd
  3. Apr 20, 2009 #2


    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Janez25! Welcome to PF! :wink:
    Yes, either will do :smile:

    now, what property (of either) means that the maximum is never reached?

    (i don't think you need the IVT for this)
  4. Apr 21, 2009 #3
    Re: Welcome to PF!

    I am not sure what property I should use. I also am not sure how to show that either function does not attain a maximum value on the interval [0,1) formally.
  5. Apr 21, 2009 #4


    User Avatar
    Science Advisor
    Homework Helper

    Hint: asssume it does attain its maximum, or any local maximum, at x = a in [0,1) …

    is that possible for x or for ex?

    what property would f(x) have if that isn't possible?
  6. Apr 22, 2009 #5
    Thanks for your help!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook