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 slope between the two points (2, f(2)) and (4, f(4)).
Using the function table provided:
f(2) = -2^2 + 12 = -4 + 12 = 8
f(4) = -4^2 + 12 = -16 + 12 = -4
Now, we calculate the slope between the two points:
Slope = (f(4) - f(2)) / (4 - 2)
Slope = (-4 - 8) / (4 - 2)
Slope = -12 / 2
Slope = -6
Therefore, the average rate of change over the interval [2,4] is -6.