Here is the graph of the function $y = \frac{x^3}{3} - \frac{x^2}{2} - 6x + \frac{5}{3}$.

• The graph shows a local maximum at the point $(-2, \frac{13}{3})$.
• It also shows a local minimum at the point $(3, -\frac{40}{3})$.

If you have any questions or need further details, feel free to ask!

Here are five related questions to consider:

1. What are inflection points, and how would you find them for this function?
2. How do you determine the concavity of a function?
3. What is the significance of the second derivative in identifying maxima and minima?
4. How can you apply this method to real-world optimization problems?
5. How does the behavior of the function change as $x \to \infty$ or $x \to -\infty$?

Tip: Always verify the nature of the critical points using the second derivative to confirm whether they are maxima, minima, or points of inflection.