I'm frustrated beyond belief with a proof. Suppose we have an continuous even function with a domain of all real numbers. Now this function has limit as x goes to negative infinty equal to l and the limit as x goes to positive infinty is also equal to l. I want to show that this function will either have a maximum or a minimum. I'm not sure at all how to show this rigorously since I don't know how to apply the definition of a limit to limits at infinity. I think it has to do with bounds. And I need to do this without first derivative test.