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To determine the inflection points of the given graph \( f(x) \), we need to identify where the concavity of the function changes. An inflection point occurs when the second derivative \( f''(x) \) changes its sign, indicating a transition from concave up to concave down, or vice versa.

From the graph:

1. At \( x = -4 \), the curve transitions from concave down to concave up. This is an inflection point.
2. At \( x = 2 \), the curve transitions from concave up to concave down. This is another inflection point.

Thus, the correct answers are:
- \( (-4, 1) \)
- \( (2, 3) \)

If you have additional questions or need further clarification, feel free to ask! Here are some follow-up questions for deeper exploration:

1. How are inflection points mathematically determined using derivatives?
2. What is the significance of concavity in real-world applications of functions?
3. Can a function have multiple inflection points in close proximity? If so, why?
4. What is the relationship between the first and second derivatives at inflection points?
5. How would this problem change if the function was not differentiable at certain points?

**Tip:** When analyzing graphs, always look for changes in the curvature to identify inflection points effectively.

Consider the following graph of f(x). Which of the following are inflection points of f? Options: (-4, 1), (-1, 2), (2, 3), (5, 1).

Understand how to identify inflection points by analyzing changes in concavity from a given graph of f(x). Learn to apply the second derivative test and determine points of transition such as (-4, 1) and (2, 3). Suitable for students in Grades 11-12.

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