Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Review - Concept Check - Page 319: 5

Answer

$(a)$ Local minimum or local maximum points stand for the maximum or minimum value that the graph of a function takes in a specific viewing rectangle. $(b)$ A graph of a function $P$, of a degree $n$ can have at most $(n-1)$ local extrema.

Work Step by Step

$(a)$ Local minimum or local maximum points stand for the maximum or minimum value that the graph of a function takes in a specific viewing rectangle. The point $(x, P(x))$ is local maximum (or minimum) point of a function, if it is the highest (or lowest) point of the graph of $P$ within specific viewing rectangle. $(b)$ In general, a graph of a function $P$, of a degree $n$ can have at most $(n-1)$ local extrema.
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