Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 1 - Precalculus Review - Chapter Review Exercises - Page 37: 29


$x=0,\ \ \ x=2,\ \ \ x=-2 $ $f (x)$ is decreasing for $x\lt -1.4 $ and $0\lt x \lt 1.4$

Work Step by Step

We are given $$f(x)=x^{4}-4 x^{2}$$ We factor and set the function equal to zero to find the roots: \begin{align*} x^{4}-4 x^{2}&=0\\ x^2(x^2-4)&=0\\ x^2(x-2)(x+2)&=0\end{align*} Thus, the roots are $$x=0,\ \ \ x=2,\ \ \ x=-2 $$ We use the figure shown below to find where $f (x)$ is decreasing: $x\lt -1.4 $ and $0\lt x \lt 1.4$
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