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

Solution:

Given, f(x) = (3x - 6) / (x - 2)

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

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)

Now, f(a) = f(6) = (3(6) - 6) / (6 - 2)

= (18 - 6) / 4

= 12 / 4

= 3

f(b) = f(8) = (3(8) - 6) / (8 - 2)

= (24 - 6) / (6)

= 18/6

= 3

Put the value of f(a) and f(b) in (1),

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

A(x) = (3 - 3) / (8 - 6)

= 0/2

A(x) = 0

Therefore, the average rate of change is 0.

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

Summary:

If f(x) = 3x - 6/x - 2, the average rate of change of f(x) over the interval [6, 8] is 0.