Hey guys,

I'm having a little trouble trying to prove a question on uniform continuity that is in one of my textbooks (which doesn't have answers, unfortunately).

The question asks:

"Is the function f(x) = x^{3}+x uniformly continuous on R? Prove your answer"

I am almost certain that the answer is no for the simple reason that as x gets increasingly large the gaps get bigger so the same epsilon value won't work, but I'm not sure as to how to go about writing this in mathematical terms.

I know that for a function to be uniformly continuous |f(x) - f(x')|<epsilon whenever |x - x'|<delta for ALL x, x' that are elements of the subset, S, which in this case is R.

I would appreciate any help although preferably a proof that I can follow so that I can make the link to what I know to how to write it, if that makes sense.

Thanks in advance,

Mark