Calculate the average rate of change over the interval [2,4] given the function table for f(x)=−x2+12 .

Question

x f(x)
1 11
2 8
3 3
4 −4 (1 point)
Responses

6
6

−2
negative 2

2
2

−6

Answer 1

The average rate of change over the interval [2,4] can be calculated using the formula:

Average Rate of Change = (f(4) - f(2)) / (4 - 2)

First, find f(4) and f(2) from the function table:

f(4) = -4
f(2) = 8

Then substitute these values into the formula:

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.