Here is the plot of $f(x) = x^3 - 2x + 1$. This function is a cubic polynomial and its behavior includes regions where it is increasing and decreasing, with inflection points.

Further Exploration

1. What is the first derivative of $f(x)$ and what does it tell us about the function's slope?
2. How can you find the critical points of $f(x)$?
3. What are the inflection points of $f(x)$?
4. How does the second derivative help in understanding the concavity of $f(x)$?
5. How can you find the antiderivative of $f(x)$?
6. What is the definite integral of $f(x)$ over a specific interval?
7. How does the graph change if you alter the coefficients in the polynomial $x^3 - 2x + 1$?
8. How can you approximate the area under the curve of $f(x)$ using numerical methods?

Tip: When sketching antiderivatives, keep in mind that regions where the original function is positive will result in increasing slopes, and regions where it is negative will result in decreasing slopes.