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

Answer:

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

Step-by-step explanation:

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

$A(x) = \frac{f(b)-f(a)}{b-a}$       ....[1]

As per the statement:

Given the function:

$f(x) = \frac{3x-6}{x-2}$

At x = 6

$f(6) = \frac{3(6)-6}{6-2}=\frac{18-6}{4}=\frac{12}{4} =3$

⇒$f(6) = 3$

At x = 8

$f(8) = \frac{3(8)-6}{8-2}=\frac{24-6}{6}=\frac{18}{6} =3$

⇒$f(8) = 3$

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;

$A(x) = \frac{f(8)-f(6)}{8-6}=\frac{3-3}{2}=\frac{0}{2} = 0$

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