calculate the average rate of change over the interval [2,4] given the function table for f(x)=-x^2+12
x / f(x)
1 / 11
2 / 8
3 / 3
4 / -4
The average rate of change over the interval [2,4] can be calculated by finding the change in f(x) over the interval and dividing it by the change in x.
Change in f(x) = f(4) - f(2) = -4 - 8 = -12
Change in x = 4 - 2 = 2
Average rate of change = Change in f(x) / Change in x
Average rate of change = -12 / 2
Average rate of change = -6
Therefore, the average rate of change over the interval [2,4] is -6.