1. The problem statement, all variables and given/known data Show that a solution to y'=y(6-y) has a an inflection point at y=3. 3. The attempt at a solution If y has an inflection point, then y''=0. I know that y'=y(6-y), and therefore i know that y''=(y(6-y))'=(6y-y2)'=6-2y So, if y''=0, and y''=6-2y then 0=6-2y => y=3. Solved. But the answer in the back of my book writes the following: "At the inflection point, y''=0. We derive each side in the equation. When we derive the right side - according to the chain rule - we should get: (y(6-y))'y'=(6y-y2)'y'=(6-2y)y' If y=3, then both the right side and thus y'' equals zero" What i dont get is why the book states that y' is a factor in the calculation: (y(6-y))'y'=(6y-y2)'y'=(6-2y)y'