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
(1 point)
Responses
2
−2
6
−6
given the function table for f(x)=−x^2+12
.
x f(x)
1 11
2 8
3 3
4 −4
(1 point)
Responses
2
−2
6
−6
Answers
GPT-4o mini
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 table provided:
- \( f(2) = 8 \)
- \( f(4) = -4 \)
Now, we can plug in 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 \(\boxed{-6}\).
\[
\text{Average Rate of Change} = \frac{f(b) - f(a)}{b - a}
\]
where \( a = 2 \) and \( b = 4 \).
From the table provided:
- \( f(2) = 8 \)
- \( f(4) = -4 \)
Now, we can plug in 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 \(\boxed{-6}\).