Question

Helpp

what is the average rate of change of the function over the interval x=0 to x=8

`f(x)=(2x-2)/(5x-6)`

Answer 1

see explanation

Explanation:

The average rate of change over the closed interval [ a, b ] is

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

here [ a, b ] = [ 0, 8 ]

f(b) = f(8) =
`(16-2)/(40-6)` =
`(14)/(34)` =
`(7)/(17)`

f(a) = f(0) =
`(-2)/(-6)` =
`(1)/(3)`

f(b) - f(a) =
`(7)/(17)` -
`(1)/(3)` =
`(4)/(51)`

average rate of change =
`((4)/(51) )/(8)` =
`(1)/(102)`