Question

Calculate the average rate of change over the interval [2,4] given the function table for: f (x) = -x^2 + 12
x | f (x)
1 | 11
2 | 8
3 | 3
4 | -4
A. 6
B. -2
C. 2
D. -6

Answer 1

To calculate the average rate of change of the function \( f(x) = -x^2 + 12 \) over the interval \([2, 4]\), we can use the formula for the average rate of change, which is:

\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]

Here, \( a = 2 \) and \( b = 4 \).

From the function table provided, we have:

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

Now, substituting these values into the formula:

\[
\text{Average Rate of Change} = \frac{f(4) - f(2)}{4 - 2} = \frac{-4 - 8}{4 - 2} = \frac{-12}{2} = -6
\]

Thus, the average rate of change over the interval \([2, 4]\) is \(-6\).

So the answer is **D. -6**.