calculate the average rate of change over the interval [2,4] given the function table for f(x)=-x^2+12
To calculate the average rate of change over the interval [2,4] for the function f(x)=-x^2+12, we first need to find the value of the function at x=2 and x=4.
When x=2:
f(2) = -2^2 + 12
f(2) = -4 + 12
f(2) = 8
When x=4:
f(4) = -4^2 + 12
f(4) = -16 + 12
f(4) = -4
Next, we can calculate the average rate of change over the interval [2,4] using the formula:
Average rate of change = (f(4) - f(2)) / (4 - 2)
Average rate of change = (-4 - 8) / (4 - 2)
Average rate of change = -12 / 2
Average rate of change = -6
Therefore, the average rate of change over the interval [2,4] for the function f(x)=-x^2+12 is -6.