Answer
Refer to the graph below.
Local maximum is $4$; local minimum is $0$
Increasing over $(-2,-1)\cup(1,2)$; decreasing over $(-1,1)$
Work Step by Step
Step 1. Use a graphing tool (in this case Desmos) to graph the given function. Input the function $f(x)=x^3-3x+2$ and set the domain $(-2, 2)$. Refer to the graph below.
Step 2. Based on the graph, we can find the local maximum of $4$ at $x=-1$ and a local minimum of $0$ at $x=1$.
Step 3. The function is increasing over $(-2,-1)\cup(1,2)$ and decreasing over $(-1,1)$.
