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: 25


$f(x)$ does not have an inverse function.

Work Step by Step

We use the power rule to find the derivative of $f(x)$. \[ f'(x) = x^3 - 4x = x(x^2-4) = x(x+2)(x-2) \] $f'(x)$ can be both positive and negative so $f(x)$ is not strictly monotonic on its entire domain.
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