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 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 will use the formula for average rate of change:

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

where \( a \) and \( b \) are the endpoints of the interval. Here, \( a = 2 \) and \( b = 4 \).

From the given function values:

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

Now we can plug these values into the formula:

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

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