Calculate the average rate of change over the interval [2,4] given the function table for f(x)=−x2+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 difference between the function values at the endpoints of the interval and dividing it by the difference in the x-values.
The function values at the endpoints are f(2) = 8 and f(4) = -4.
The difference in the y-values is -4 - 8 = -12.
The difference in the x-values is 4 - 2 = 2.
Therefore, the average rate of change over the interval [2,4] is -12/2 = -6.