Finding relative extremes, i need help with my homework for calculus?

heres what i've had so far

heres the function

f(x) = x / x - 1...... i derived it which came out to f'(x) = -1 / (x - 1)^2..... I set the denominator equal to zero to solve for the critical number, the critical number is x = 1.... then i used a number line to determine where the function is increasing or decreasing to verify that 1 is a relative extrema.... but the problem is when i plug in the numbers to the left of 1 and the numbers to the right of 1, i get negative numbers which indicates that the function is decreasing, what should i do? is there not a relative max or min?? im very confused...

Re: Finding relative extremes, i need help with my homework for calculus?

The domain of this function is $\displaystyle (-\infty, 1) \cap (1, \infty) $ This function is not defined at x = 1, so no derivative exists at x=1 but the derivative does exist for $\displaystyle f(x) | x \in (-\infty, 1) \cap (1, \infty)$. But the derivative $\displaystyle f'(x) = - \frac{1}{(x-1)^2} $ is not equal to zero for any point in the domain, so no relative extrema exists.