After deriving f(x) = (x+2)/x, I got -2/(x^2)..
How do I find the absolute extrema if there are no critical numbers?
You can see that -2/x² is always negative, whatever x is. Hence the function is strictly decreasing.
So if you consider the interval [1,2], the absolute maximum will be at 1 and the absolute minimum will be at 2.
Now you should get back to the definition of a critical point. It's a point where the derivative is 0 or a point where the derivative is undefined.
So x=0 is a critical point.
But yes, it doesn't give any extrema.
An absolute minimum can be found by looking at the limit of the function as x goes to infinity. The function will always be "above" this value.