Answer
Refer to the graph below.
Local maximum $=0$;
Local minimum $=-0.25$;
increasing over $(-0.71,0)\cup(0.71,2)$;
decreasing over $(2,-0.71)\cup(0,0.71)$
Work Step by Step
Step 1. Use a graphing utility and input $f(x)=x^4-x^2$. Set the domain to $(-2, 2)$. Refer to the graph below..
Step 2. Based on the graph, we can find the local maximum of $0$ at $x=0$ and local minimum of $-0,25$ at $x\approx-0.71$ and $x\approx0.71$.
Step 3. The function is increasing over $(-0.71,0)\cup(0.71,2)$, and decreasing over $(2,-0.71)\cup(0,0.71)$.
