Calculate the average rate of change over the interval [2,4} given the function table for f(x)=−x^2+12
To find the average rate of change over the interval [2,4] for the function f(x) = -x^2 + 12, we first need to calculate the values of the function at the endpoints of the interval.
f(2) = -2^2 + 12 = -4 + 12 = 8
f(4) = -4^2 + 12 = -16 + 12 = -4
Now, we can calculate the average rate of change over the interval [2,4] by using the formula:
Average Rate of Change = (f(4) - f(2)) / (4 - 2)
= (-4 - 8) / (2)
= -12 / 2
= -6
Therefore, the average rate of change of the function f(x) = -x^2 + 12 over the interval [2,4] is -6.