Functions Modeling Change: A Preparation for Calculus, 5th Edition

Published by Wiley
ISBN 10: 1118583191
ISBN 13: 978-1-11858-319-7

Chapter 2 - Functions - 2.6 Concavity - Exercises and Problems for Section 2.6 - Exercises and Problems - Page 106: 2

Answer

It appears that a graph of this function would be concave up, because the average rate of change becomes less negative as $t$ increases.

Work Step by Step

To determine concavity, we calculate the rate of change: $$ \begin{gathered} \frac{\Delta f(t)}{\Delta t}=\frac{10-20}{1-0}=-10 . \\ \frac{\Delta f(t)}{\Delta t}=\frac{6-10}{2-1}=-4 . \\ \frac{\Delta f(t)}{\Delta t}=\frac{3-6}{3-2}=-3 . \\ \frac{\Delta f(t)}{\Delta t}=\frac{1-3}{4-3}=-2 . \end{gathered} $$ It appears that a graph of this function would be concave up, because the average rate of change becomes less negative as $t$ increases.
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