Theory and ExamplesLet ƒ be a function defined on an

Chapter 4, Problem 70E

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QUESTION:

Problem 70E

Theory and Examples

Let ƒ be a function defined on an interval [a, b]. What conditions could you place on ƒ to guarantee that

 where min  and max refer to the minimum and maximum

values of on [a, b]? Give reasons for your answers.

Questions & Answers

QUESTION:

Problem 70E

Theory and Examples

Let ƒ be a function defined on an interval [a, b]. What conditions could you place on ƒ to guarantee that

 where min  and max refer to the minimum and maximum

values of on [a, b]? Give reasons for your answers.

ANSWER:

Solution

Step 1 of 3

In this problem we have to prove that ƒ be a function defined on an interval [a, b]. What conditions could you place on ƒ to guarantee that

 

The condition is that should be continuous over and differentiating on


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