Calculus 10th Edition

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

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.3 Exercises - Page 343: 23


$f(x)$ has an inverse function.

Work Step by Step

We use the power rule to find: \[ f'(x) = -3x^2 -1 \] $x^2$ is always positive so $-3x^2$ is always positive. Therefore, $f'(x)$ is always negative, and $f(x)$ is strictly monotonic (it is always decreasing).
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