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Determine the interval(s) for which the function shown below is decreasing.



To determine the intervals where the function is decreasing, we need to identify the segments of the graph where the function moves downward as we move from left to right.

From the graph:

1. The function decreases from \( x = -\infty \) until it reaches the local minimum at around \( x = -4 \).
2. The function increases between \( x = -4 \) and \( x = 1 \).
3. The function then decreases again between \( x = 1 \) and \( x = 4 \).
4. After \( x = 4 \), the function starts increasing again.

### Therefore, the intervals where the function is decreasing are:
- \( (-\infty, -4] \)
- \( (1, 4] \)

Would you like more details or have any questions? 

Here are 5 follow-up questions you might consider:
1. How can you determine intervals of increase and decrease using the derivative of a function?
2. What are critical points, and how do they relate to increasing and decreasing intervals?
3. Can you find the exact coordinates of the local minima and maxima?
4. How can you determine concavity and points of inflection from the graph?
5. What is the significance of the global maximum and minimum in a function?

**Tip:** To find where a function is increasing or decreasing, you can take its derivative and analyze where the derivative is positive or negative.

Determine the interval(s) for which the function shown below is decreasing.

Learn how to determine the intervals where a function is decreasing by analyzing its graph. This solution explores the use of the first derivative test and critical points to find the intervals of decrease for the given function. Suitable for students in Grades 11-12.

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