Here is the graph of the function $f(x) = 2x^3 - 4x^2 + x + 2$. It shows the behavior of the cubic polynomial, including its local maxima and minima, and the overall shape of the curve.

Would you like further details about this graph, such as finding the critical points, the derivative, or analyzing its behavior at specific values? Let me know if you have any questions!

Here are 5 related questions to explore further:

1. What are the critical points of the function $f(x) = 2x^3 - 4x^2 + x + 2$?
2. How can you find the inflection points of $f(x)$?
3. What is the derivative of the function $f(x) = 2x^3 - 4x^2 + x + 2$?
4. How do you determine the global and local behavior of the cubic function?
5. How can you find the roots of the cubic equation $f(x) = 0$?

Tip: To find the critical points of a function, you first take its derivative and then solve for $x$ where the derivative equals zero. These points indicate local maxima, minima, or saddle points.