Answer
Refer to the graph below.
Local maximum is $5$; local minimum is $1$
Increasing at $(-1,0)\cup(2,3)$; decreasing at $(0,2)$
Work Step by Step
Step 1. Use a graphing tool (in this case Desmos) and input $f(x)=x^3-3x^2+5$. Set the domain as $(-1, 3)$. Refer to the graph below.
Step 2. Based on the graph, we can find the local maximum as $5$ at $x=0$, and the local minimum is $1$ at $x=2$.
Step 3. The function is increasing at $(-1,0)\cup(2,3)$ and decreasing at $(0,2)$.
