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.