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All the local maximum and minimum values of the function and the value of x at which each occurs.

From the graph of the function you provided, we can identify the local maxima and minima by observing the peaks and valleys of the curve.

### Observations:
1. **Local Maxima** occur where the graph has a peak.
2. **Local Minima** occur where the graph has a valley.

### Local Maxima:
- **First local maximum** appears at approximately \( x = -2 \), and the value of the function at this point is roughly \( y = 2 \).
- **Second local maximum** appears at approximately \( x = 2.5 \), and the value of the function at this point is roughly \( y = 2 \).

### Local Minima:
- **First local minimum** occurs at approximately \( x = 0 \), and the function value at this point is \( y = -2 \).
- **Second local minimum** occurs at approximately \( x = 4 \), and the function value at this point is about \( y = -1 \).

### Summary:
- Local maxima: \( x \approx -2, 2.5 \) with \( y = 2 \).
- Local minima: \( x \approx 0, 4 \) with \( y = -2 \) and \( y = -1 \), respectively.

Let me know if you'd like further clarification or any additional details!

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Here are 5 related questions you might explore:
1. What is the difference between absolute and local extrema?
2. How do you determine concavity using the second derivative?
3. What is the relationship between critical points and local extrema?
4. How can you find the exact location of extrema analytically using derivatives?
5. How do you identify inflection points in a function?

**Tip:** When analyzing graphs, looking at where the derivative equals zero (horizontal tangents) helps locate potential maxima and minima.

Analyze the local maxima and minima of a function by observing its graph. Learn how to locate critical points where the graph reaches peaks and valleys. Suitable for students in Grades 11-12 studying calculus and graph analysis.

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