Answer
Refer to the graph below.
local maxima $\approx-0.52$ and $\approx-1.87$;
local minimum $=-2$;
increasing over $(-3,-1.57)\cup(0,0.64)$;
decreasing over $(-1.57,0)\cup(0.64,2)$
Work Step by Step
Step 1. Use a graphing utility and input $f(x)=-0.4x^4-0.5x^3+0.8x^2-2$ over the specified region. Set the domain to $(-3, 2)$.
Step 2. Based on the graph, we can find the local maxima of $\approx-0.52$ at $x\approx -1.57$ and $\approx-1.87$ at $x\approx0.64$, and a local minimum of $-2$ at $x=0$.
Step 3. The function is increasing over $(-3,-1.57)\cup(0,0.64)$, and decreasing over $(-1.57,0)\cup(0.64,2)$.
