Question

How do you find the average rate of change for the function `F(x)=7+ 4/(x+3)` on the indicated intervals [-2, -2+h]?

Answer 1

Average rate of change of `F` on interval `[a,b]` is `(F(b)-F(a))/(b-a)`

Explanation:

So, the average rate of change for the function `F(x)=7+ 4/(x+3)` on the indicated intervals `[-2, -2+h]` is:

`(F(-2+h)-F(-2))/((-2+h)-(-2))`

`= ([7+ 4/((-2+h)+3)] -[7+ 4/((-2)+3)])/((-2+h)-(-2)`

`= (4/(h+1) - 4/1)/h`

`= ((4-4(1+h))/(1+h))/(h/1)`

`= (-h)/(h+1) * 1/h`

`= (-1)/(h+1)`
(The last line is equal the preceding lines for `x != 0`)