Answer
Refer to the graph below.
Local maximum is $\approx 0.19$; local minimum is $\approx-0.19$
Increasing over $(-2,-0.77)\cup(0.77,2)$; decreasing over $(-0.77,0.77)$
Work Step by Step
Step 1. Use a graphing utility (Desmos in this case) and input $f(x)=x^5-x^3$Set the domain as $(-2, 2)$. Refer to the graph below.
Step 2. Based on the graph, we can find the local maximum is approximately $0.19$ at $x\approx -0.77$ and the local minimum is approximately $-0.19$ at $x\approx 0.77$.
Step 3. The function is increasing over $(-2,-0.77)\cup(0.77,2)$ and decreasing over $(-0.77,0.77)$.
