Find two numbers whose sum is 9 if the product of one by the square of the other is a maximum

Answer 1

x+y = 9
the product z is
z = xy^2 = x(9-x)^2 = 81x - 18x^2 + x^3
dz/dx = 81 - 36x + 3x^2 = 3(x^2-12x+27)
dz/dx=0 when x = 3 or 9
Pick x=3, so y=6