The function you've provided is:

\[
f(x) = x^3 - 6x^2 + 4x - 12
\]

What would you like to do with this function? Here are a few things we can explore:

1. **Find the roots** (solve \(f(x) = 0\))
2. **Find the derivative** (for slope, critical points, etc.)
3. **Find the second derivative** (for concavity and inflection points)
4. **Graph the function** (to visualize behavior)
5. **Evaluate the function** (at specific points)

Would you like to explore one of these options or something else?

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Here are 5 related questions:

1. What are the roots of \(f(x) = 0\)?
2. What are the critical points of \(f(x)\)?
3. Where is the function increasing or decreasing?
4. Where does the function change concavity (inflection points)?
5. What is the end behavior of \(f(x)\) as \(x \to \infty\) and \(x \to -\infty\)?

**Tip:** The first derivative of a function gives you information about its increasing or decreasing nature!

Explore how to solve and analyze the cubic function f(x) = x^3 - 6x^2 + 4x - 12. This guide covers finding the roots, analyzing the function's increasing or decreasing intervals, determining inflection points, and understanding its end behavior. Suitable for Grades 10-12 students.

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