To find the average rate of change of a function over a given interval, we need to calculate the change in the function over that interval, and divide by the length of the interval.
In this case, we want to find the average rate of change of the function f(x) = 12x - 4.8x^2 over the interval [0,5].
First, we need to find the value of the function at the endpoints of the interval:
f(0) = 12(0) - 4.8(0)^2 = 0
f(5) = 12(5) - 4.8(5)^2 = -72
Next, we calculate the change in the function over the interval:
Change in f(x) = f(5) - f(0) = -72 - 0 = -72
Finally, we divide the change in the function by the length of the interval:
Average rate of change = (Change in f(x)) / (Length of interval) = (-72) / (5-0) = -14.4
Therefore, the average rate of change of the function f(x) = 12x - 4.8x^2 over the interval [0,5] is -14.4.