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The question asks to find the open intervals where the derivative \( f'(x) \) is negative, based on the graph of \( f(x) \) shown.

To find where \( f'(x) \) is negative, we need to look at the intervals where the graph of \( f(x) \) is decreasing. This is because the derivative \( f'(x) \) represents the slope of the function, and where the slope is negative, the function is decreasing.

From the graph, we can observe the following:

- \( f(x) \) is decreasing between approximately \( x = -3 \) and \( x = 1 \), where the curve slopes downward.

So the open interval where \( f'(x) \) is negative is:
\[
(-3, 1)
\]

This is the interval where \( f(x) \) is decreasing.

Would you like more details or clarifications on this? Here are five follow-up questions related to this problem:

1. What is the significance of the derivative being positive or negative for a function?
2. How can we determine critical points on a graph like this?
3. What does it mean if the derivative is zero at a point?
4. How would you find where the function is increasing using the graph of \( f(x) \)?
5. How do you interpret inflection points in terms of the second derivative?

**Tip**: Remember that the sign of the derivative tells you whether a function is increasing or decreasing. If the derivative is negative, the function is going down; if it's positive, the function is going up.

Consider the graph of y = f(x) shown in blue. Find the open interval(s) where f'(x) is negative.

Learn how to identify the open intervals where the derivative f'(x) is negative by analyzing the graph of the function f(x). This problem involves basic calculus concepts such as the first derivative and increasing/decreasing functions. Suitable for high school students in Grades 10-12.

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