Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.1 Maximum and Minimum Values - 3.1 Execises - Page 211: 24


By use the graph of $f (x) = |x|$ , to find the absolute and local maximum and minimum values of f. The sketch of the graph of f in the interval [-5,5] is shown below:

Work Step by Step

The absolute maximum or absolute minimum occurs at the end points of the interval. And local maximum and local minimum occurs between the end points of the interval. But from the graph, observe that the minimum of f does not occurs at the end point of the interval [-5,5]. So the absolute minimum and the local minimum are coincides. It is given as, f(0)=0. Also, from the graph, observe that the absolute maximum and local maximum does not exist.
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