The result below is not very known:
Let f:I -> R be differentiable on the open (non empty) interval I. Then, there exists a subinterval of I where f is Lipschitz.
Actually I think this is true under a less rigid assumption. I think the conclusion remains true if, instead of full differentiabilty on I, we assume the existence of the Dini derivatives, that is, suppose that, for every x of I, f is differentiable at least at x+ or x-, not necessarily at both.
2007-10-25
06:20:04
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2 answers
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asked by
Steiner
7