Math Help - Supremum and maximum

Can anyone provide an example of a differentiable function f(x) such that a supremum of f exists but a maximum of f does not exist, for (k is any fixed number)?

Thanks very much.

Originally Posted by WWTL@WHL

Can anyone provide an example of a differentiable function f(x) such that a supremum of f exists but a maximum of f does not exist, for (k is any fixed number)?

Thanks very much.

Wait, this question doesn't make sense. It is wrong. Are you sure that it's the right question?

It's not a question I've been set, but it's just something I've been thinking about.

So I guess you're telling me there is no such function? Could you kindly explain why?

Originally Posted by WWTL@WHL

It's not a question I've been set, but it's just something I've been thinking about.

So I guess you're telling me there is no such function? Could you kindly explain why?

The real reasoning? Continuous(and thus differentiable) functions preserve compactness. Or, more simply Extreme value theorem - Wikipedia, the free encyclopedia