https://file.aiquickdraw.com/mathbot/file/17305713976399w8sibht.jpg

Let's analyze each statement in relation to the graph and determine which ones are true:

1. **Statement A: \( f(x) \) has exactly one singular point.**
   - A singular point typically refers to a point where the function’s derivative does not exist. In this graph, we don't observe any points where the curve is discontinuous or has a cusp. However, there are critical points where the slope of the tangent is zero (such as at points B and C). Since there isn’t a non-differentiable point, this statement **is false**.

2. **Statement B: \( f(x) \) is decreasing everywhere.**
   - The function decreases from point A to B and then again from C to D, but it increases from B to C. Therefore, \( f(x) \) is **not decreasing everywhere**, so this statement **is false**.

3. **Statement C: \( f(x) \) has no critical points.**
   - Critical points are points where the derivative is zero or undefined. In this graph, points B and C are critical points where the slope of the tangent is zero. Thus, \( f(x) \) does have critical points, and this statement **is false**.

4. **Statement D: \( f(x) \) is decreasing on the interval (C, D).**
   - Observing the interval between points C and D, the graph is indeed decreasing. This statement is **true**.

5. **Statement E: \( f(x) \) has an absolute minimum at D.**
   - The lowest point on the graph is point D, making it the absolute minimum on the interval \([A, D]\). This statement is **true**.

6. **Statement F: \( f(x) \) has a local minimum at B.**
   - Point B represents a local minimum because it is lower than the points immediately around it. Therefore, this statement is **true**.

### Summary:
The statements that are **true** are:
- **D.** \( f(x) \) is decreasing on the interval (C, D).
- **E.** \( f(x) \) has an absolute minimum at D.
- **F.** \( f(x) \) has a local minimum at B.

Would you like more details on any of these statements or further clarification?

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### Related Questions:
1. How can we identify singular points versus critical points in a function's graph?
2. What are the characteristics of increasing and decreasing intervals on a graph?
3. How can we determine absolute and local extrema in a function?
4. What other methods are there to find critical points besides visual inspection?
5. How does the presence of critical points affect the continuity and differentiability of a function?

### Tip:
When analyzing graphs, remember that a function is decreasing on intervals where the graph slopes downwards from left to right.

Select ALL statements that are TRUE about f(x) on the closed interval [A, D] based on this graph.

Explore the analysis of f(x) on the closed interval [A, D] to identify true statements about its critical points, decreasing intervals, and local and absolute minima. This solution involves calculus concepts like critical points and the First Derivative Test, suitable for Grades 11-12.

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