Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 3 - Applications of Differentiation - 3.4 Exercises - Page 192: 2

Answer

$f'(x) < 0$ $f''(x) > 0$

Work Step by Step

1.) Determine the algebraic sign (Either positive or negative) of $f'(x)$ Since the graph of $f(x)$ is decreasing, $f'(x) < 0$ ($f'(x)$ is less than zero and therefore negative) 2.) Determine the algebraic sign of $f''(x)$ Since the graph of $f(x)$ opens up on the interval, $f(x)$ is concave up for this interval and $f''(x) > 0$ (positive). We can also tell that $f''(x)$ is positive because as $f(x)$ decreases it decreases less and less as x increases ($f(x)$ is decreasing at a decreasing rate) which means even though $f'(x)$ is negative, it is increasing and is approaching zero.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.