Question

What is the average rate of change of the function over the interval x = 0 to x = 8?
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Answer 1

The average rate of change is:

`(13)/(161)`

Explanation:

The rational function given to us is;

`f(x)=(3x+4)/(2x+7)`

`f(0)=(3(0)+4)/(2(0)+7)`

`f(0)=(4)/(7)`

`f(8)=(3(8)+4)/(2(8)+7)`

`f(0)=(28)/(23)=1`

The average rate of change of this function from x=0 to x=8 is the slope of the secant line connecting:

(0,f(0)) and (8,f(8))

Average rate of change =
`=(f(8)-f(0))/(8-0)`

`=((28)/(23)-(4)/(7) )/(8)`

`=(13)/(161)`