Answer
$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 $0\lt x \lt 1.4$
