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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

    tiny-tim

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    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

    tiny-tim

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    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!
     
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