Answer
Refer to the graph below.
local maximum $\approx-1.91$;
local minimum $\approx-18.89$;
increasing over $(-3.77,1.77)$;
decreasing over $(-6,-3.77)\cup(1.77,4)$
Work Step by Step
Step 1. Use a graphing utility and input $f(x)=-0.2x^3-0.6x^2+4x-6$. Set the domain as $9-6, 4)$. Refer to the graph below.
Step 2. Based on the graph, we can find the local maximum as approximately $-1.91$ at $x\approx-3.77$ and the local minimum of approximately $-18.89$ at $x\approx1.77$.
Step 3. The function is increasing over $(-3.77,1.77)$ and decreasing over $(-6,-3.77)\cup(1.77,4)$.
