Question
For each interval in the table, indicate whether the function is increasing, decreasing, or neither increasing nor decreasing over the interval.
Increasing
Decreasing
Neither Increasing or Decreasing
−7<x<−3−7<x<−3
−3<x<−1−3<x<−1
−1<x<1−1<x<1
1<x<31<x<3
3<x<53<x<5
5<x<75<x<7
Increasing
Decreasing
Neither Increasing or Decreasing
−7<x<−3−7<x<−3
−3<x<−1−3<x<−1
−1<x<1−1<x<1
1<x<31<x<3
3<x<53<x<5
5<x<75<x<7
Answers
Answered by
GPT-4o mini
To determine whether the function is increasing, decreasing, or neither in each interval, I would typically need the actual function or some context about how the function behaves within those intervals. Since I don't have that information, I will explain how you could analyze any specific function in those intervals, or you can provide me with the function to analyze it directly.
1. **Choose the function:** You should start with the function you are analyzing.
2. **Find the derivative:** The derivative of the function will indicate where the function is increasing or decreasing. If \( f'(x) > 0 \) in an interval, then the function is increasing in that interval. If \( f'(x) < 0 \), then the function is decreasing. If \( f'(x) = 0 \), then the function might be constant or have critical points.
3. **Test points:** You can select test points from each interval to evaluate the derivative.
Please provide the function or context regarding its behavior, and I can help determine the nature of the intervals you mentioned.
1. **Choose the function:** You should start with the function you are analyzing.
2. **Find the derivative:** The derivative of the function will indicate where the function is increasing or decreasing. If \( f'(x) > 0 \) in an interval, then the function is increasing in that interval. If \( f'(x) < 0 \), then the function is decreasing. If \( f'(x) = 0 \), then the function might be constant or have critical points.
3. **Test points:** You can select test points from each interval to evaluate the derivative.
Please provide the function or context regarding its behavior, and I can help determine the nature of the intervals you mentioned.