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To determine the intervals where \( f(x) \geq 0 \), we will examine the graph and identify where the function lies on or above the x-axis (i.e., where the function is either positive or zero).

From the graph:

- The function crosses the x-axis at approximately \( x = -6 \), \( x = -1 \), \( x = 5 \).
- The function is above or on the x-axis in the intervals:
  - From \( x = -6 \) to \( x = -1 \) (including the points where \( f(x) = 0 \), i.e., \( x = -6 \) and \( x = -1 \)).
  - From \( x = 5 \) onwards (since the function remains positive beyond \( x = 5 \)).

Thus, the intervals where \( f(x) \geq 0 \) are:

\[
[-6, -1] \cup [5, \infty)
\]

Let me know if you'd like any further clarifications or details!

### Related Questions:
1. How do we determine the intervals where a function is decreasing?
2. How can we use the derivative to find where \( f(x) \geq 0 \)?
3. What happens when a function crosses the x-axis more than twice?
4. How can concavity affect the intervals where \( f(x) \geq 0 \)?
5. How can we apply this analysis to real-world problems like profit functions?

**Tip:** When solving graph-based questions, always identify the critical points (such as where the graph crosses the x-axis) to break down the intervals.

Determine all intervals on which f(x) ≥ 0.

Learn how to determine the intervals where a function f(x) is greater than or equal to zero by analyzing a graph. This problem covers key concepts in function behavior and graph analysis, suitable for students in Grades 9-12.

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