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.

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- Nov 16th 2011, 10:03 AMArythAnalysis Question
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. - Nov 16th 2011, 10:10 AMPlatoRe: Analysis Question