University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 3 - Practice Exercises - Page 204: 119


Graph B represents $f(x)$ and graph A represents $f'(x)$.

Work Step by Step

As the derivative $f'(x)$ represents the change in the form of the function $f(x)$, examining the graph of $f'(x)$ shows clues about the graph of $f(x)$. Looking at these two graphs, we notice the followings: - The area where graph A is positive, graph B is increasing; and where graph A is negative, graph B is decreasing. We know that the sign of $f'(x)$ represents whether $f(x)$ is rising or falling. - Graph A reaches $0$ where graph B changes direction and appears to have a horizontal tangent. It is also known that $f(x)$ has a horizontal tangent where $f'(x)=0$. We therefore can conclude that graph B represents $f(x)$ while graph A represents $f'(x)$.
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