Question

What is the average rate of change of the function over the interval x = 0 to x = 6? f(x) = (2x - 1) / (3x + 5)

Answer 1

The average rate of change of the function over the interval x = 0 to x = 6 is
`(34)/(195)`.

Explanation:

Geometrically speaking, the average rate of change (
`r`) of the function over a given interval is determined by equation of secant line, that is:

`r = (f(b)-f(a))/(b-a)` (1)

Where:

`a`,
`b` - Lower and upper bounds.

`f(a)`,
`f(b)` - Function evaluated at lower and upper bounds.

If we know that
`f(x) = (2\cdot x -1 )/(3\cdot x + 5)`,
`a = 0` and
`b = 6`, then the average rate of change of the function over the interval is:

`f(a) = (2\cdot (0)-1)/(3\cdot (0) +5)`

`f(a) = -(1)/(5)`

`f(b) = (2\cdot (6)-1)/(3\cdot (6)+5)`

`f(b) = (11)/(13)`

`r = ((11)/(13)-\left(-(1)/(5) \right) )/(6-0)`

`r = (34)/(195)`

The average rate of change of the function over the interval x = 0 to x = 6 is
`(34)/(195)`.