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: 120


Graph A represents $f(x)$ and graph $B$ 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: - Both graphs are on the positive side, but one graph is falling while the other is rising. Graph A rises but more and more slowly as $x\to\infty$, while at the same time, graph $B$ falls more and more slowly as well. Derivative shows the rate of change of a function. The fall of the graph of $f'(x)$ shows that $f(x)$ is changing a slower and slower rate. - Graph B seems to approach infinity as $x\to0$, while graph A appears to have a vertical tangent there (though we do not see the negative side of the $x-$axis). $f(x)$ will have a vertical tangent when $f'(x)$ is not defined. We therefore can conclude that graph A represents $f(x)$ while graph B represents $f'(x)$.
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