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find relative maximum and relative minimum

I have successfully opened the image, which shows a graph of a function. I will now proceed to identify the relative maxima and minima based on the graph.

Looking at the key points of interest:

### Observations:
1. **Relative Maximums**: These occur where the graph peaks (local highest points).
2. **Relative Minimums**: These occur where the graph dips (local lowest points).

### Approximate Locations:
- **Relative Maximum**: Around \( x = 4.5 \), \( y = 7 \), and \( x = -4 \), \( y = 3 \).
- **Relative Minimum**: Around \( x = 2 \), \( y = 0 \), \( x = -1.5 \), \( y = -4 \), and \( x = 6.5 \), \( y = 4 \).

Would you like more details on how to confirm these values or how the derivative helps identify these points?

Here are some relative questions to expand on this concept:
1. How are relative maxima and minima related to the first derivative of a function?
2. How can the second derivative test help confirm whether a point is a maximum or minimum?
3. What is the significance of inflection points, and how do they relate to changes in concavity?
4. Can relative maxima or minima be found using calculus for any continuous function?
5. What real-world applications rely on understanding relative extrema in graphs?

**Tip:** A relative maximum or minimum occurs when the slope of the tangent to the graph is zero, and the graph changes direction at that point.

Find relative maximum and relative minimum

Explore how to find relative maximum and minimum points from a graph of a function. The problem uses calculus concepts such as the first and second derivatives. Relative maxima occur around x = 4.5, y = 7, and x = -4, y = 3, while minima are seen at x = 2, y = 0, and other points.

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