Answer
See graph below.
local maximum $\approx1.53$
local minima $\approx0.54$ and $\approx-3.57$
increasing on $(-0.34,0.41)\cup(1.80,3)$
decreasing on $(-2,-0.34)\cup(0.41,1.80)$
Work Step by Step
Step $1$. Use a graphing utility and input $f(x)=2x^4-5x^3+2x+1$. Refer to the graph below.
Step $2$. From the graph, we can find a local maximum of $\approx1.53$ at $x\approx41$ and local minima of $\approx0.54$ at $x\approx-0.34$ and $\approx -0357$ at $x\approx1.80$.
Step $3$. From the graph, we can find the function increasing on $(-0.34,0.41)\cup(1.80,3)$ and decreasing on $(-2,-0.34)\cup(0.41,1.80)$.
