I have my real analysis final tomorrow and there are multiple choice questions. I'm wondering about a fast way to tell if a function is uniformly continuous or not. I know and understand the definition of uniform continuity, and I understand its difference from continuity, but I'm realizing I don't really know how to tell if a function is uniformly continuous or not (on a given interval or on R).
One of my classmates suggested that a function is NOT uniformly continuous if its derivative diverges in the given interval. Is this true? Can I just think of the graph of the function and if its slope does not eventually settle to some point, is it not uniformly continuous?
Thanks in advance for any help regarding how to approach these kinds of questions!
Best Answer
Some common situations:
A continuous function $f$ is uniformly continuous if
A function $f$ is not uniformly continuous if
Outside of that, I'd say just go back to the definition. I hope you find this helpful.