Calculate the average rate of change over the interval [2,4] given the function table for f(x)=−x^2+12.
To calculate the average rate of change over the interval [2, 4], we need to find the difference in the function values at the endpoints and divide it by the difference in the input values.
The function table for f(x) = -x^2 + 12 is as follows:
x | f(x)
-------
2 | 8
3 | 3
4 | 0
The difference in the function values at the endpoints is f(4) - f(2) = 0 - 8 = -8.
The difference in the input values is 4 - 2 = 2.
Therefore, the average rate of change over the interval [2, 4] is -8/2 = -4.