Question

Calculate the average rate of change of f(x) = 1 x - x2 - 2 for 3 ≤ x ≤ 6. A) -163 18 B) -18 163 C) 163 18 D) 18 163

Answer 1

The answer is A.)-163/18

Answer 2

To solve this we are going to use the average rate of change formula:
`A(x)= (f(b)-f(a))/(b-a)`
where

`A(x)` is the average rate of change of the function

`f(a)` is the position function evaluated at
`a`

`f(b)` is the position function evaluated at
`b`

`a` is the first point in the interval

`b` is the second point in the interval

We can infer for our problem that the first point is 3 and the second point is 6, so
`a=3` and
`b=6`. Lets replace those values in our formula:

`A(x)= (f(b)-f(a))/(b-a)`

`A(x)= (f(6)-f(3))/(6-3)`

`A(x)= (6-6^2-2-(3-3^2-2))/(3)`

`A(x)= (-32-(-8))/(3)`

`A(x)= (-32+8)/(3)`

`A(x)= (-24)/(3)`

`A(x)=-8`

We can conclude that the average rate of change of the function f(x) = 1 x - x2 - 2 for 3 ≤ x ≤ 6 is -8