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Analysis homework help

  • Thread starter Janez25
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  • #1
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Homework Statement



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

Homework Equations





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.
 

Answers and Replies

  • #2
tiny-tim
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Welcome to PF!

Hi Janez25! Welcome to PF! :wink:
… 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.
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)
 
  • #3
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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.
 
  • #4
tiny-tim
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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.
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?
 
  • #5
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Thanks for your help!
 

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