We are given a random variable x with a pdf f(x) and F(x) is its distribution function. Let $$r(x) = \frac {xf(x)} {1-F(x)} $$
Then for $x< e^{\mu} $ and $$f(x) = \frac {e^ {1/2(\log x - \mu)^2}} {x (2 \pi)^{1/2}}$$
Is the function r(x) increasing, decreasing or constant in x?
I can't understand how to solve this- am I supposed to derive the F(x) function- replace it in the r(x) function and differentiate to find out? Because I tried that and got lost in the middle. Also wasn't sure if that was the right way to approach this question.