Question

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

x f(x)

1 11
2 8
3 3
4 −4

Responses:

−6

−2

6

2

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:

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

where \( a = 2 \) and \( b = 4 \).

From the function table provided, we know:

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

Now we can substitute 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 \(-6\).

The correct response is:

\(-6\)