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: 24


$f(x)$ has an inverse function.

Work Step by Step

We use the power rule to find the derivative of $f(x)$. \[ f'(x) = 3x^2 - 12x+12 \] We complete the square to get: \[ f'(x) = 3(x-2)^2 \] We see that $f'(x)$ is always nonzero because $(x-2)^2$ is always nonzero so $f(x)$ is strictly monotonic.
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