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 air. Estimate the average rate of change over the interval [0.7,4.3] .(1 point)
To find the average rate of change over the interval [0.7, 4.3], we need to calculate the change in height and change in time over that interval.
First, we find the height of the soccer ball at x=0.7 and x=4.3:
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 and change in time:
Change in height = 20.21 - 5.81 = 14.4
Change in time = 4.3 - 0.7 = 3.6
Finally, we find the average rate of change by dividing the change in height by the change in time:
Average rate of change = 14.4 / 3.6 = 4
Therefore, the average rate of change of the height of the soccer ball over the interval [0.7, 4.3] is 4 feet per second.