Homework Statement
A function f:(a,b)\to R is said to be uniformly differentiable iff f is differentiable on (a,b) and for each \epsilon > 0, there is a \delta > 0 such that 0 < |x - y| < \delta and x,y \in (a,b) imply that \left|\frac{f(x) - f(y)}{x - y}-f'(x)\right| < \epsilon.
Prove that...