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## Homework Statement

True or False: Every function on [0,1] attains its maximum

I was working on a practice midterm, and this question stumped me

## The Attempt at a Solution

I know that by "every function on [0,1]" means that dom f = [0,1] but what exactly does it mean by "attains its maximum" simply that it has a limit, as in, it doesn't approach +∞?

If this is what it means, it would be false, correct? Because you could have a function that approaches ±∞ as it approaches 1 from below.

For instance, take f(x)=[itex]\frac{1}{1-x}[/itex]