Question

How do you find the average rate of change for the function `f(x) = 2 / (x+1)` on the indicated intervals [0,h]?

Answer 1

Average rate of change `= -2/(h+1)`

Explanation:

The average rate of change for a continuous function `f(x)` over an interval is
`color(white)("XXX")("the change in "f(x)" between the endpoints")/("width of the interval")`

In this case:
`color(white)("XXX")(color(red)(f(h))-color(blue)(f(0)))/color(green)((h-0))`

`color(white)("XXX")(color(red)((2/(h+1))) - color(blue)(2/(0+1)))/color(green)(h)`

`color(white)("XXX")(color(red)(2/(h+1))-color(blue)((2h+2)/(h+1)))/color(green)(h)`

`color(white)("XXX")=((-2h)/(h+1))/color(green)(h)`

`color(white)("XXX")=-2/(h+1)`