Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 4 - Section 4.3 - How Derivatives Affect the Shape of a Graph - 4.3 Exercises: 66

Answer

$f'\lt0$ and $f''\gt0$.

Work Step by Step

Take $f(x)$ to represent the SAT scores mentioned. SAT scores are declining at a slower rate. So first, the graph of $f$ representing SAT scores must be declining, which means $f'\lt0$. Now we notice the phrase 'decline at a slower rate'. That means it declines less rapidly than it did before. The graph would therefore go from decreasing steeply, to decreasing less steeply. This means all the tangent lines are below the graph $f$. There is a concave upward here. (The image below represents a model of the graph) Therefore, $f''\gt0$.
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