Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.3 How Derivatives Affect the Shape of a Graph - 3.3 Exercises - Page 230: 57

Answer

$K(3) − K(2)>K(8) − K(7)$ $K$ concave downward.

Work Step by Step

Most students learn more in the third hour of studying than in the eighth hour, so $K(3) − K(2)$ is larger than $K(8) − K(7)$. In other words, as you begin studying for a test, the rate of knowledge gain is large and then starts to taper off, so $K'(t)$ decreases and the graph of $K$ is concave downward.
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