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(1 point)
Responses
2
2
−2
negative 2
−6
negative 6
6
To calculate the average rate of change over the interval [2,4], we need to find the change in f(x) over that interval and divide 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 = -12 / 2 = -6
Therefore, the average rate of change over the interval [2,4] is -6.