I have a quasi-concave bounded function $f: [0, \infty) \rightarrow [0,1]$. The question is whether $f*f'$ is monotonic, or under which additional conditions one could make such a statement? Thanks a lot!

What exactly is denoted by $f*f'$ here?
– fedjaNov 2 '12 at 12:42

By f * f' I mean the product of f and its first derivative (f is a function of a single variable). I am sorry for the ambiguity in the original question. Also it seems clear that this product is not monotonic in general, but which additional conditions would be needed?
– GarfieldNov 22 '12 at 8:59