Question

How do you find the critical points if `f'(x)=2-x/(x+2)^3`?

Answer 1

You need to solve: `2-x/(x+2)^3 = 0` Which has no rational and only one real, solution.

If you intended to type: `f'(x) = (2-x)/(x+2)^3`, the we're in better luck.

A critical number is a value in the domain of `f` at which the derivative is either `0` or fails to exist.

It looks as if the domain for the original `f` was `RR - {-2}`.

`f'(-2) does not exist, but`-2`is not in the domain of`f#, so it is not a critical point.

`(2-x)/(x+2)^3=0` when `2-x=0` which happens at `x=2`.

Assuming that `2` is in the domain of `f`, it is a critical point.