Answer
$${\text{No relative extrema}}$$
Work Step by Step
$$\eqalign{
& f\left( x \right) = \frac{x}{{x - 1}} \cr
& {\text{*Calculate the first derivative}} \cr
& f'\left( x \right) = \frac{d}{{dx}}\left[ {\frac{x}{{x - 1}}} \right] \cr
& f'\left( x \right) = \frac{{x - 1 - x}}{{{{\left( {x - 1} \right)}^2}}} \cr
& f'\left( x \right) = - \frac{1}{{{{\left( {x - 1} \right)}^2}}} \cr
& {\text{Set }}f'\left( x \right) = 0 \cr
& - \frac{1}{{{{\left( {x - 1} \right)}^2}}} = 0 \cr
& {\text{There are no values at which }}f'\left( x \right) = 0,{\text{ so there are no}} \cr
& {\text{relative extrema}}{\text{.}} \cr} $$
