Answer
Refer to the graph below.
local maximum $=3$;
local minima $\approx0.95$ and $\approx2.65$;
increasing over $(-1.87,0)\cup(0.97,2)$;
decreasing over $(-3,-1.87)\cup(0,0.97)$
Work Step by Step
Step 1. Use a graphing utility and input $f(x)=0.25x^4+0.3x^3-0.9x^2+3$.Set the domain to $(-3, 2)$. Refer to the graph below.
Step 2. Based on the graph, we can find the local maximum of $3$ at $x=0$ and local minima of $\approx0.95$ at $x\approx -1.87$ and $\approx2.65$ at $x\approx0.97$,
Step 3. The function is increasing over $(-1.87,0)\cup(0.97,2)$ and decreasing over $(-3,-1.87)\cup(0,0.97)$.
