Question

Maximize Q = xy^2, where x and y are positive numbers, such that x + y^2 = 4.

Answer 1

Hello,

x+y²=4==>y²=4-x
Max(Q=xy²)=Max(Q=x(4-x))=Max(Q=4x-x²)

Q'(x)=4-2x =0
==>x=4/2=2 ==>y²=4-2=2==>y=√2 since y>0

Q''(x)=-2==>a maximum.