First derivative can be found using the quotient rule.
`f'(x) = ((x-1)*1 - x*x)/(x-1)^2`
`f'(x) = (-x^2+x-1)/(x-1)^2`
At critical points, f'(x) = 0
Roots can be found by the using the standard equation for quadratic roots.
`x = (-1+-sqrt(1^2-4*(-1)*(-1)))/(2*(-1))`
`x = (-1+-sqrt(-7))/-2`
There are no real roots, therefore, f(x) doesn't have any critical points.