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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.