The function you've provided is:

\[
F(x) = \frac{6}{4} - x^3
\]

We can simplify the constant term:

\[
F(x) = 1.5 - x^3
\]

This represents a cubic function where the \( x^3 \) term dominates as \( x \) increases, and the constant 1.5 shifts the graph vertically.

Would you like to know more details, such as how to find its roots or its behavior (e.g., increasing/decreasing intervals, inflection points)?

Here are five related questions to deepen understanding:
1. What are the roots of the function \( F(x) = 1.5 - x^3 \)?
2. How do you find the derivative of \( F(x) \), and what does it tell us about the function's slope?
3. What are the critical points of \( F(x) \), and how do you classify them?
4. How does the graph of \( F(x) \) behave for large positive and negative values of \( x \)?
5. Can we determine where the function is concave up or concave down?

**Tip:** The cubic term \( x^3 \) grows quickly, so it dominates the behavior of the function for large \( |x| \).

Explore the cubic function F(x) = 1.5 - x^3, including its roots, derivative, and behavior at large values of x. This problem focuses on key algebraic concepts and function analysis, suitable for students in Grades 9-12.

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