Use the image to answer the question.

Question

A coordinate plane for f of x versus x.

Given the graph of f(x)
, on which interval is the average rate of change the greatest?

(1 point)
Responses

The function has the greatest average rate of change over the interval [4,5]
.
The function has the greatest average rate of change over the interval left bracket 4 comma 5 right bracket .

The function has the greatest average rate of change over the interval [0,1]
.
The function has the greatest average rate of change over the interval left bracket 0 comma 1 right bracket .

The function has the greatest average rate of change over the interval [5,6]
.
The function has the greatest average rate of change over the interval left bracket 5 comma 6 right bracket .

The function has the greatest average rate of change over the interval [1,4]
.
The function has the greatest average rate of change over the interval left bracket 1 comma 4 right bracket .

Answer 1

To determine the interval where the average rate of change of the function \( f(x) \) is the greatest, we typically look for the interval where the slope (change in \( f(x) \) over the change in \( x \)) is steepest.

If you can provide information such as the values of \( f(x) \) at different points on the graph or a description of the curve, I can help identify the correct interval. If the graph is providing a clear trend, the steeper the segment of the line between two points, the greater the average rate of change.

Please let me know how the graph looks or any key points from it for me to assist you further.