Analysis homework help

• Janez25
In summary, the conversation discusses finding a continuous function g: from the interval [0,1) to R that does not attain a maximum value. The suggested functions are g(x)=x and g(x)=e^x, and the task is to prove that they do not attain a maximum value using the IVT.

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.

Welcome to PF!

Hi Janez25! Welcome to PF!
Janez25 said:
… 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.

Janez25 said:
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?