To identify the local maxima and minima from the graph, we need to look for points where the function changes direction — specifically, where the slope of the graph changes from positive to negative (for a local maximum) or from negative to positive (for a local minimum).

### **Local Maxima:**
A local maximum is a point where the function reaches a peak. The slope changes from positive (going up) to negative (going down) at this point.

- **Around \( x = -1 \)**: The graph appears to have a peak around \( x = -1 \). This point is a local maximum because the graph rises before this point and falls after it. The approximate coordinates are \( (-1, 2) \).

### **Local Minima:**
A local minimum is a point where the function reaches a trough. The slope changes from negative (going down) to positive (going up) at this point.

- **Around \( x = -3 \)**: The graph appears to have a trough around \( x = -3 \). This point is a local minimum because the graph falls before this point and rises after it. The approximate coordinates are \( (-3, -2) \).

- **Around \( x = 1 \)**: The graph also has a local minimum around \( x = 1 \). The graph falls before this point and rises afterward, making it a local minimum. The approximate coordinates are \( (1, -3) \).

### **Summary:**
- **Local Maximum:** \( (-1, 2) \)
- **Local Minima:** \( (-3, -2) \) and \( (1, -3) \)

Would you like further details on how to interpret these points, or do you have additional questions about the graph?

### Relative Questions:
1. How can you determine whether a critical point is a maximum or minimum just by looking at the graph?
2. What are the differences between absolute and local maxima/minima?
3. How would you find the x-intercepts on this graph?
4. Can a function have more than one local maximum or minimum?
5. What does the behavior of the function between the local maxima and minima tell you about the function's overall trend?

### Tip:
When analyzing local maxima and minima, consider also looking at the first derivative (if available), as it gives a precise mathematical way to confirm these points.

Learn how to identify local maxima and minima in graphs with a detailed step-by-step guide. This problem involves analyzing changes in the slope of a function to pinpoint points of local maximum and minimum. Suitable for advanced high school or college-level students.

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