Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 3 - The Derivative In Graphing And Applications - 3.1 Analysis Of Functions I: Increase, Decrease, and Concavity - Exercises Set 3.1 - Page 196: 59

Answer

See explanation.

Work Step by Step

The temperature has been increasing for a while (i.e. Winter ends and Spring approaches), and then the approaching storm decreases temperature. The graph can indicate concavity up for when the temperature rises, and concavity down when the storm begins to approach. This change in concavity demonstrates the existence of an inflection point. This is not always necessarily the case, but assumptions should be made to answer the question. An alternative solution is to explain how morning temperatures are cooler than afternoon temperatures, so as the temperature increases somewhat exponentially (demonstrating upward concavity), the approaching storm would decrease it, requiring the graph to change concavity.
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