Calculus: Early Transcendentals 8th Edition

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

Chapter 2 - Review - Exercises - Page 168: 48


Curve a is the graph of $f$, curve b is the graph of $f''$, curve c is the graph of $f'$.

Work Step by Step

First look at curve b. Curve b has 3 local extremas (the point where the curve changes from going up to down and vice versa) and 2 times passes the $Ox$ line. Imagine if curve b represents $f$ or $f'$, there must be another curve that passes the $Ox$ 3 times to match the 3 local extremas of curve b. However, none of the remaining curves passes the $Ox$ 3 times. Therefore, curve b is the graph of $f''$. Now look at the remaining 2 curves. Curve c has 2 local extremas and 1 time passes the $Ox$ line. If curve c represents $f$, then curve a must pass the $Ox$ line 2 times to match the 2 local extremas of curve c. However, curve a does not pass the $Ox$ line at all. Therefore, curve c is the graph of $f'$ and curve a is the graph of $f$.
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