The function
h(x)=x+ln(1−x)
is defined on the interval (−∞,1).
(i) Compute h′(x) and find all critical points that lie in (−∞,1).
(ii) Examine the sign of h′(x) on each relevant interval and identify any local extremum of h.
(iii) Give the exact value of h at every point of local extremum obtained in part (ii).