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

(1 point)
Responses

2
2

−6
negative 6

−2
negative 2

6
6
Skip to navigation

Answer 1

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

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

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

From the function table provided:

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

Now we can plug these values into the formula:

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

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

The correct response is:

**−6** (negative 6)