calculate the average rate of change over the interval [2,4] given the function table for f(x)=-x^2+12.
2
-2
-6
6
To calculate the average rate of change over the interval [2,4], we need to find the change in the function values divided by the change in x-values.
First, find the function values for x=2 and x=4:
f(2) = -2^2 + 12 = -4 + 12 = 8
f(4) = -4^2 + 12 = -16 + 12 = -4
Now, find the change in function values:
Change in f(x): -4 - 8 = -12
Next, find the change in x-values:
Change in x: 4 - 2 = 2
Now, calculate the average rate of change:
Average rate of change = Change in f(x) / Change in x
Average rate of change = -12 / 2
Average rate of change = -6
Therefore, the average rate of change over the interval [2,4] is -6.