Question

If ,f(x)=3x-6/x-2 what is the average rate of change of f(x) over the interval [6, 8]?

Answer 1

i hope this helps you



f (x)= 3 (x-2)/(x-2)


f (x)= 3


f(6)= 3


f (8)= 3

Answer 2

the average rate of change of f(x) over the interval [6, 8] is, 0

Explanation:

Average rate of change (A(x)) of f(x) over interval [a, b] is given by:

`A(x) = (f(b)-f(a))/(b-a)` ....[1]

As per the statement:

Given the function:

`f(x) = (3x-6)/(x-2)`

At x = 6

`f(6) = (3(6)-6)/(6-2)=(18-6)/(4)=(12)/(4) =3`

⇒
`f(6) = 3`

At x = 8

`f(8) = (3(8)-6)/(8-2)=(24-6)/(6)=(18)/(6) =3`

⇒
`f(8) = 3`

We have to find the average rate of change of f(x) over the interval [6, 8]

Substitute the given values in [1] we have;

`A(x) = (f(8)-f(6))/(8-6)=(3-3)/(2)=(0)/(2) = 0`

Therefore, the average rate of change of f(x) over the interval [6, 8] is, 0