Answer
Refer to graph below.
local maximum $\approx4.04$
local minimum $\approx-2.04$.
increasing on $(-3,-0.91)\cup(0.91,3)$
decreasing on $(-0.91,0.91)$
Work Step by Step
Step 1. Use a graphing utility and input $f(x)=2x^3-5x+1$. (Refer to graph below.)
Step 2. From the graph, we can find a local maximum of $\approx4.04$ at $x\approx-0.91$ and a local minimum of $\approx-2.04$ at $x\approx0.91$.
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Step 3. From the graph, we can find the function increasing on $(-3,-0.91)\cup(0.91,3)$ and decreasing on $(-0.91,0.91)$.
