University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Section 4.1 - Extreme Values of Functions - Exercises - Page 215: 15

Answer

The function has an absolute minimum at $x=0$ but does not have any absolute maximum.

Work Step by Step

$$f(x)=|x|\hspace{2cm}-1\lt x\lt2$$ The graph is sketched below. - The graph obviously has an absolute minimum value, which is $f(0)=0$. - The graph, however, does not have an absolute maximum value. The graph does seem to reach the highest point at $x=2$, but since we consider here the interval $(-1,2)$, we do not include the point where $x=2$. And since there are no other maximum values, the graph does not have any absolute maximum in the defined interval. This answer is still consistent with Theorem 1, because Theorem 1 requires that the function $f$ in question be examined in a CLOSED interval, not an open one like in this case.
Small 1543167934
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.