Question

What is the interval where f(x)= 1/( x+2) -1 is increasing and decreasing?

`f(x)= 1/ (x+2) -1`

Answer 1

Evaluate the derivative of the function:

`(df)/dx = -1/(x+2)^2`

The derivative is negative everywhere except for `x = -2` where it is not defined, so `f(x)` is monotone decreasing in the intervals `(-oo,-2)` and `(-2,+oo)`.

graph{1/(x+2)-1 [-10, 10, -5, 5]}