Answer
Refer to the graph below.
local maximum $\approx3.25$;
local minimum $\approx-4.05$;
increasing over $(-1.16,2.16)$;
decreasing over $(-4,-1.16)\cup(2.16,5)$
Work Step by Step
Step 1. Use a graphing utility and input $f(x)=-0.4x^3+0.6x^2+3x-2$. Set the domain to $(-4, 5)$. Refer to the image below.
Step 2. Based on the graph, we can find the local maximum of $\approx3.25$ at $x\approx2.16$ and a local minimum of $\approx-4.05$ at $x\approx-1.16$.
Step 3. The function is increasing over $(-1.16,2.16)$ and decreasing over $(-4,-1.16)\cup(2.16,5)$.
