Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 2 - Nonlinear Functions - Chapter Review - Review Exercises - Page 113: 21

Answer

1. the maximum number of turning points, 2. the end behavior of the graph (far left and far right ends), 3. which way the graph points (up or down) when x gets large.

Work Step by Step

Properties of Polynomial Functions 1. A polynomial function of degree $n$ can have at most $n-1$ turning points. Conversely, if the graph of a polynomial function has $n$ turning points, it must have degree at least $n+1$. 2. In the graph of a polynomial function of even degree, both ends go up or both ends go down. For a polynomial function of odd degree, one end goes up and one end goes down. 3. If the graph goes up as $x$ becomes large, the leading coefficient must be positive. If the graph goes down as $x$ becomes large, the leading coefficient is negative. So we can determine: 1. the maximum number of turning points, 2. the end behavior of the graph (far left and far right ends), 3. which way the graph points (up or down) when x gets large.
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