The sum of the two numbers is k. the product of one by the square of the other is to be a maximum . What is one of the numbers?

1 answer

x+y=k
p = xy^2 = (k-y)y^2 = ky^2 - y^3
dp/dy = 2ky - 3y^2
dp/dy=0 when y = 2k/3