# Analysis homework help

## Homework Statement

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

## 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.

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tiny-tim
Homework Helper
Welcome to PF!

Hi Janez25! Welcome to PF!
… 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

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

(i don't think you need the IVT for this)

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.

tiny-tim
Homework Helper
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?