Question

Let J ⊂ be an interval. Let f : J → R be differentiable with

bounded derivative, that is, |f
(x)| ≤ L for some L > 0. Then f is Lipschitz with

Lipschitz constant L. In particular, f is uniformly continuous on J. Hint: Recall

the mean value theorem​

Answer 1

Answer:

Let J ⊂ be an interval. Let f: J → R be differentiable with bounded derivative, that is, |f (x)| ≤ L for some L > 0. Then f is Lipschitz with Lipschitz constant L. In particular, f is uniformly continuous on J. Hint: Recall the mean value theorem (Theorem 4.2.5). ... If f is not uniformly continuous, then there exists ε > 0 such that for ...

Step-by-step explanation:

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