To find the average rate of change over the interval [0.7, 4.3], we need to calculate the change in height over this time interval and then divide it by the change in time.
First, we need to find the height of the soccer ball at the beginning and end of the interval:
f(0.7) = - (0.7)^2 + 9(0.7) = -0.49 + 6.3 = 5.81
f(4.3) = - (4.3)^2 + 9(4.3) = -18.49 + 38.7 = 20.21
Next, we calculate the change in height:
Change in height = f(4.3) - f(0.7) = 20.21 - 5.81 = 14.4
Next, we calculate the change in time:
Change in time = 4.3 - 0.7 = 3.6
Finally, we calculate the average rate of change:
Average rate of change = Change in height / Change in time = 14.4 / 3.6 = 4
Therefore, the average rate of change over the interval [0.7, 4.3] is 4 feet per second.
The height (in feet) of a soccer ball that was kicked is modeled by the function f(x) = - x ^ 2 + 9x where x is time (in seconds) that the ball was in the airEstimate the average rate of change over the interval [0.7, 4.3]
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