Calculate the average rate of change over the interval [2,4] given the function table for f(x)=−x2 12 .
−6 negative
− 2 negative
2
6
To find the average rate of change over the interval [2,4] for the function f(x) = -x^2/12, we need to calculate the difference in the function values at the endpoints of the interval and divide by the difference in the x-values.
The function table gives the following values for f(x):
-6: negative
-2: negative
2
6
The function values at the endpoints of the interval are:
f(2) = -(2^2)/12 = -4/12 = -1/3
f(4) = -(4^2)/12 = -16/12 = -4/3
The difference in function values is:
(-4/3) - (-1/3) = -4/3 + 1/3 = -3/3 = -1
The difference in x-values is:
4 - 2 = 2
Therefore, the average rate of change over the interval [2,4] is:
-1 / 2 = -1/2