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