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

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