Uniformly Continuous Functions and Mean Value Theorem
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Assume that f is differentiable for each x and there exists M>0
such that
for each x
Prove that f is uniformly continuous on D.
Hint: Can use the mean value theorem.
keywords: differentiability, continuity
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By assumption, there exists M∈R such that |f'(x)| for all x∈R. By the Mean Value Theorem, if x<y ∈ R ...
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