Respuesta :
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:
[tex]A(x) = \frac{f(b)-f(a)}{b-a}[/tex] ....[1]
As per the statement:
Given the function:
[tex]f(x) = \frac{3x-6}{x-2}[/tex]
At x = 6
[tex]f(6) = \frac{3(6)-6}{6-2}=\frac{18-6}{4}=\frac{12}{4} =3[/tex]
⇒[tex]f(6) = 3[/tex]
At x = 8
[tex]f(8) = \frac{3(8)-6}{8-2}=\frac{24-6}{6}=\frac{18}{6} =3[/tex]
⇒[tex]f(8) = 3[/tex]
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;
[tex]A(x) = \frac{f(8)-f(6)}{8-6}=\frac{3-3}{2}=\frac{0}{2} = 0[/tex]
Therefore, the average rate of change of f(x) over the interval [6, 8] is, 0
