f(x)= ln(1-ln(x)) a) indicate where f(x) is decreasing using interval notation b)Use interval notation to indicate where f(x) is concave down

1 Answer

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

a) You need to remember that the function decreases if `f'(x)lt0`  and the function increases if `f'(x)gt0` , hence you need to evaluate `f'(x)`  and to solve the inequalities above such that:

`f'(x) = (1/(1-lnx))*(1-ln x)'`

`f'(x) = -1/(x(1-lnx))` 

Notice that for any value of `x in (0,oo), ` the values of derivative are negative, hence, the function decreases over `(0,oo).`