The function h(x)=x+ (1-x) is defined on the interval

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The function

h(x)=x+\ln(1-x)

is defined on the interval

(-\infty,1)

. (i) Compute

h'(x)

and find all critical points that lie in

(-\infty,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).