The average rate of change of the function h over the interval (2, 6) is determined to be 3/4. This value represents the slope of the secant line connecting the points (2, 4) and (6, 7) on the graph.
In the graph you sent me, the function is represented by a blue curve. The interval (2, 6) is marked on the x-axis with two red dots. The secant line that intersects the graph at these two points is also shown in blue.
To find the slope of the secant line, we need to find the coordinates of its two endpoints. The endpoint on the left side of the graph is at (2, 4), and the endpoint on the right side of the graph is at (6, 7).
Once we have the coordinates of the two endpoints, we can use the slope formula to calculate the slope of the line:
m = (y2 - y1) / (x2 - x1)
where:
m is the slope of the line
(x1, y1) are the coordinates of the first endpoint
(x2, y2) are the coordinates of the second endpoint
Plugging in the values we found, we get:
m = (7 - 4) / (6 - 2) = 3 / 4
Therefore, the average rate of change of h over the interval (2, 6) is 3/4.