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

2
2

6
6

−6
negative 6
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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 table you've provided, we can read the function values:

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

Now, we 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:

$-6$

So the correct response is:

−6