Question
A coordinate plane for f of x versus x.
Describe the behavior of the function by determining over which interval the function has a negative average rate of change.
(1 point)
The average rate of change is negative over the interval [
,
].
Describe the behavior of the function by determining over which interval the function has a negative average rate of change.
(1 point)
The average rate of change is negative over the interval [
,
].
Answers
GPT-4o mini
To determine the interval over which the function \( f(x) \) has a negative average rate of change, we need to consider the definition of the average rate of change. The average rate of change of a function \( f(x) \) over an interval \([a, b]\) can be calculated using the formula:
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
For the average rate of change to be negative, \( f(b) - f(a) \) must be less than 0, which implies that \( f(b) < f(a) \). This means that the function \( f(x) \) is decreasing over the interval \([a, b]\).
To find the specific interval where this occurs, you would need to examine the graph of the function \( f(x) \) or have information about the behavior of \( f(x) \) over specific intervals.
Without a specific function or graph provided, I cannot determine the exact interval. However, if you have access to the graph or function of \( f(x) \), look for the segments where the graph is decreasing.
Once you identify the interval \([a, b]\) where the function is decreasing, you can conclude:
The average rate of change is negative over the interval \([a, b]\).
Please provide additional information or data about the function \( f(x) \) if you want a more precise analysis.
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
For the average rate of change to be negative, \( f(b) - f(a) \) must be less than 0, which implies that \( f(b) < f(a) \). This means that the function \( f(x) \) is decreasing over the interval \([a, b]\).
To find the specific interval where this occurs, you would need to examine the graph of the function \( f(x) \) or have information about the behavior of \( f(x) \) over specific intervals.
Without a specific function or graph provided, I cannot determine the exact interval. However, if you have access to the graph or function of \( f(x) \), look for the segments where the graph is decreasing.
Once you identify the interval \([a, b]\) where the function is decreasing, you can conclude:
The average rate of change is negative over the interval \([a, b]\).
Please provide additional information or data about the function \( f(x) \) if you want a more precise analysis.