https://file.aiquickdraw.com/mathbot/file/173022324081200wzu60u.jpg

https://file.aiquickdraw.com/mathbot/file/17302232408129k31yljo.jpg

Based on the graph and options provided in your images, let’s analyze each statement about the function \( f(x) \) on the interval \([A, D]\):

1. **Option A: \( f(x) \) has a local minimum at \( C \)**  
   - At point \( C \), the function appears to reach a low point locally. Therefore, \( C \) can indeed be considered a local minimum.
   - **True**

2. **Option B: \( f(x) \) has exactly two critical points on \([A, D]\)**  
   - Critical points occur where the derivative \( f'(x) = 0 \) or is undefined. Observing the graph, it seems there are two such points, one at \( B \) (local maximum) and another at \( C \) (local minimum).
   - **True**

3. **Option C: \( f(x) \) is decreasing on the interval \((A, B)\)**  
   - From \( A \) to \( B \), the graph of \( f(x) \) shows a downward trend, indicating that the function is indeed decreasing on this interval.
   - **True**

4. **Option D: \( f(x) \) has no absolute minimum**  
   - \( C \) appears to be the lowest point on the graph within the interval \([A, D]\), which would make it an absolute minimum.
   - **False**

5. **Option E: \( f(x) \) has an absolute minimum at \( C \)**  
   - Since \( C \) is the lowest point within the interval \([A, D]\), it serves as the absolute minimum for \( f(x) \) over this interval.
   - **True**

6. **Option F: \( f(x) \) has an absolute maximum at a critical point**  
   - The absolute maximum occurs at \( D \), which does not appear to be a critical point (no horizontal tangent or undefined derivative). Thus, the absolute maximum is not at a critical point.
   - **False**

### Final True Statements:
The statements that are

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

Analyze the graph of f(x) on the interval [A, D] to determine true statements about critical points, local minimums, and absolute maximums. This problem uses concepts from calculus, including the first derivative test and the Extreme Value Theorem.

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