# problem with bounded quasi concave function

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!

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What exactly is denoted by $f*f'$ here? –  fedja Nov 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? –  Garfield Nov 22 '12 at 8:59