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: 26

Answer

$f(x)$ has an inverse function.

Work Step by Step

We use the power rule to find the derivative of $f(x)$. \[ f'(x) = 5x^4 + 6x^2 = x^2(5x^2+6) \] Both $x^2$ and $5x^2+6$ are always positive so $f'(x)$ is always positive. Therefore, $f(x)$ is strictly monotonic.
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