Calculate the average rate of change over the interval [2,4]

Question

given the function table for f(x)=−x2+12
.

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

−2
negative 2

6
6

2
2

−6

Answer 1

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

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

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

From the function table, we can find:

• \( f(2) = 8 \)
• \( f(4) = -4 \)

Now, 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.