Calculus: Early Transcendentals 8th Edition

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

Chapter 4 - Review - True-False Quiz - Page 358: 10



Work Step by Step

For $x$: $f(x)\lt 0$: the function is below x-axis. $f'(x)\lt 0$: the function is always decreasing. $f''(x)\gt 0$: function is always concave up. This is impossible because a function cannot be negative, decreasing and concave up for all $x$ while not having its left end go up above the $x-axis$ toward $\infty$. Function does not exist. Hence, the given statement is false.
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