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To determine which of the statements are true based on the graph of \( f' \):

1. **Relative Min at \( x = -3 \)**:
   - A relative minimum of \( f \) occurs where \( f' \) changes from negative to positive.
   - At \( x = -3 \), \( f' \) is increasing (it changes from negative to positive).

2. **Point of Inflection at \( x = 2 \)**:
   - A point of inflection of \( f \) occurs where \( f'' \) (the second derivative) changes sign, which corresponds to \( f' \) having a local extremum (either a max or min).
   - At \( x = 2 \), \( f' \) has a local minimum, indicating that \( f'' \) changes sign, so there is a point of inflection at \( x = 2 \).

3. **Concave Down for \( 0 < x < 4 \)**:
   - \( f \) is concave down where \( f'' < 0 \), which corresponds to \( f' \) being decreasing.
   - For \( 0 < x < 4 \), \( f' \) is indeed decreasing, indicating \( f \) is concave down in this interval.

Based on the above analysis, all three statements are true:

- **I** is true because \( f \) has a relative minimum at \( x = -3 \).
- **II** is true because the graph of \( f \) has a point of inflection at \( x = 2 \).
- **III** is true because the graph of \( f \) is concave down for \( 0 < x < 4 \).

Therefore, the correct answer is:

**All three statements (I, II, and III) are true.**

Would you like more details or have any questions?

Here are some questions you might ask next:
1. Can you explain how to identify points of inflection on a graph of \( f' \)?
2. How do you determine concavity from the graph of \( f' \)?
3. What are the key features to look for on the graph of a derivative?
4. Can you give an example of how to find relative extrema using the first derivative?
5. How does the behavior of \( f' \) relate to the concavity of \( f \)?

**Tip**: When analyzing the graph of a derivative, remember that points where the derivative changes sign can indicate relative extrema of the original function.

Learn how to analyze derivative graphs to identify relative minima, points of inflection, and concavity. This problem involves using the first and second derivative tests to interpret the behavior of functions. Suitable for advanced high school and college-level students.

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