calculus question

Question

A rumor spreads through a school according to the differential equation  . What percentage of the school has heard the rumor when it is spreading the fastest?

	75
	50
	25
	Cannot be determined

Answer 1

dy/dx is quadratic in y, with a < 0 so dy/dx will have a max at its vertex:

dy/dx has zeros at y = 0 and y = .5 so its vertex is the average of those, y = .25 or 25%