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Use the graph of the function f(x) = x3 + x2 − x − 1 to identify its relative maximum and minimum.

To identify the relative maximum and minimum of the function \( f(x) = x^3 + x^2 - x - 1 \) using the graph:

1. **Relative Maximum**: This occurs at the highest point of a turning region on the graph. From the image, it appears there is no clear peak above the x-axis, indicating there is no relative maximum.

2. **Relative Minimum**: The graph shows a clear turning point around \( x = -1 \) where the graph dips below the x-axis before rising again. This point, based on the shape, would be the relative minimum.

Thus, the relative minimum occurs near \( x = -1 \), where \( f(x) \) reaches its lowest point locally.

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### Relative Questions:
1. How do we calculate exact relative extrema using calculus?
2. What is the derivative of the given function?
3. How do we distinguish between relative maximum and minimum using the second derivative test?
4. Can the function have absolute extrema if it is a cubic polynomial?
5. How does the shape of cubic functions generally behave in terms of turning points?

### Tip:
When identifying relative extrema graphically, look for points where the slope of the function changes sign, indicating a transition from increasing to decreasing or vice versa.

Use the graph of the function f(x) = x^3 + x^2 − x − 1 to identify its relative maximum and minimum.

Identify the relative maximum and minimum for the cubic function f(x) = x^3 + x^2 − x − 1 by analyzing its graph. Learn about calculus concepts such as the first and second derivative tests for finding local extrema. Suitable for Grades 10-12.

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