Suppose $\displaystyle f : (a,b) \to R$ is differentiable and $\displaystyle | f'(x)|\leq M, \forall x \in (a,b)$. Prove that f is uniformly continuous on (a,b).
I am having trouble finding a starting point. Any help would be appreciated.
Suppose $\displaystyle f : (a,b) \to R$ is differentiable and $\displaystyle | f'(x)|\leq M, \forall x \in (a,b)$. Prove that f is uniformly continuous on (a,b).
I am having trouble finding a starting point. Any help would be appreciated.