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Let f R-->R be differentiable. If |f'(x)|<M< oo, then f is uniformly continuous, e.g.,

by the MVTheorem. Is this conditions necessary too, i.e., if f:R-->R is differentiable

and uniformly continuous, does it follow that |f'(x)|<M<oo ?

Thanks.

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# Uniform continuity and Bounded Derivative

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