# extension of log concave functions

So I need to prove something or see if its true and I don't know how to write in nice math text because this is my first question, so please bear with me

We have a CDF $F_h(s)$ for $0\le s\le 1$. The corresponding density $f_h$ is increasing, convex, and Log-concave. Prove that if there exists $t\in(0,\frac12)$ s.t. $$\frac{f_h'(t)}{f_h(t)+1} > \frac{f_h'(1-t)}{f_h(1-t)+1}$$ then for every $t'\in(t,\frac12)$ we also have $$\frac{f_h'(t')}{f_h(t')+1} > \frac{f_h'(1-t')}{f_h(1-t')+1}$$

Any help would be greatly appreciated. Thanks

• Do you have a source for the question? – wolfies Oct 26 '14 at 12:25
• no its my question...from research... – Daniel Oct 26 '14 at 18:55