15. Let I be an interval. Prove that if f is differentiable on I and if the derivative f' is bounded on I, then f satisfies a Lipschitz condition on I. (See Definition 5.4.4.)
15. Let I be an interval. Prove that if f is differentiable on I and if the derivative f' is bounded on I, then f satisfies a Lipschitz condition on I. (See Definition 5.4.4.)
College Algebra (MindTap Course List)
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Chapter3: Functions
Section3.3: More On Functions; Piecewise-defined Functions
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![15. Let I be an interval. Prove that if fis differentiable on I and if the derivative f is bounded on I,
then f satisfies a Lipschitz condition on I. (See Definition 5.4.4.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe3ac779f-6ea4-42fb-bae3-9116a1a09906%2Fdd86f6d3-a563-4d70-a8d5-d0f8adec70ae%2Fkmz8fcd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:15. Let I be an interval. Prove that if fis differentiable on I and if the derivative f is bounded on I,
then f satisfies a Lipschitz condition on I. (See Definition 5.4.4.)
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