The sign of the derivative is always positive ( remember o(1-o) and 0<o<1). What is important is the general shape of derivative: maximumal at 0.5, minimal at the extremes. I have replaced the derivative with other functions ( d(x)=c, d(x)=cx, d(x)=min(x,1-x), d(x)=x(1-x)+c ) and bp works when there is a bump. John Kolen