Answer
Refer to the graph below.
local maxima: $\approx-0.86$ and $\approx15.55$;
local minimum: $2$
increasing on $(-5,-0.85)U(0,2.35)$, decreasing on $(-0.85,0)U(2.35,5)$
Work Step by Step
Step $1$. Use a graphing utility and input $f(x)=-x^4+2x^3+4x^2-2$. Locate relative maximum and relative minimum values. Refer to the graph below.
Step $2$. We can approximate the local maxima as $-0.86$ and $f15.55$, and the local minimum is $-2$.
Step $3$. Using the graph we can identify the function is increasing on $(-5,-0.85)\cup(0,2.35)$ and decreasing on $(-0.85,0)\cup(2.35,5)$
