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Chapter 3: Q. 5 (page 287)

Suppose f is a function that is defined and continuous on an open interval I. Will the endpoints of I always be local extrema of f ? Will f necessarily have a global maximum or minimum in the interval I? Justify your answers.

Short Answer

Expert verified

The endpoints of I always be local extrema off because there will not be any endpoint extrema.The function f may or may not be a global maximum (or minimum) on the interval

Step by step solution

01

Step 1. Given information.

We have to explain that : Suppose f is a function that is defined and continuous on an open interval I. Will the endpoints of I always be local extrema of f ? Will f necessarily have a global maximum or minimum in the interval I?

02

Step 2. Explanation

It is given that f is a function that is defined and continuous on an open interval I

The endpoints of I always be local extrema off because there will not be any endpoint extrema.

The function f may or may not be a global maximum (or minimum) on the interval

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