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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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).`

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial