Let f be defined on an interval 1. Suppose that there exists m > 0 and a> 0 such that: |f(x) – f(y)| < m|x – y|ª for all x, y E I (Such a function is said to satisfy a Lipschitz condition of order a on I. c) Show by example that a=1, then f is not necessarily differentiable on I.

Let f be defined on an interval 1. Suppose that there exists m > 0 and a> 0 such that: |f(x) – f(y)| < m|x – y|ª for all x, y E I (Such a function is said to satisfy a Lipschitz condition of order a on I. c) Show by example that a=1, then f is not necessarily differentiable on I.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Let f be defined on an interval I. Suppose that there exists m > 0 and
a> 0 such that: |f(x) – f(y)| < m|x – yla for all x, y E I (Such a
function is said to satisfy a Lipschitz condition of order a on I.
c) Show by example that a=1, then f is not necessarily differentiable
on I.

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