Question

Please help:What is the average rate of change of the function over the interval x = 0 to x = 8?f (x) = 2x−2 / 5x−6Enter your answer, as a fraction, in the box.

Answer 1

The average rate of change from x = a to x = b is:

`(f(b)-f(a))/(b-a)`

In this question:

a = 0

b = 8

So, let's find f(a) = f(0):

`\begin{gathered} f(x)=(2x-2)/(5x-6) \\ f(0)=(2*0-2)/(5*0-6) \\ f(0)=(-2)/(-6)=(1)/(3) \end{gathered}`

Now, let's find f(b) = f(8):

`\begin{gathered} f(8)=(2*8-2)/(5*8-6) \\ f(8)=(16-2)/(40-6) \\ f(8)=(14)/(34) \\ f(8)=(7)/(17) \end{gathered}`

Substituting the values in the first equation:

`\begin{gathered} (f(b)-f(a))/(b-a) \\ (f(8)-f(a))/(8-0) \\ ((7)/(17)-(1)/(3))/(8) \\ ((21-17)/(17*3))/(8) \\ ((4)/(51))/(8)=(4)/(51)*(1)/(8) \\ =(1)/(102) \end{gathered}`

Answer: 1/102.