Question

Maximize Q = xy2, where x and y are positive numbers, such that x + y2 = 4.

Answer 1

y^2=4-x
Q=x(4-x)=4x-x^2
Q'=4-2x
set Q'=0 to find critcal numbers
4-2x=0
so x=2
then y^2=4-2=2 so y=sqrt(2)
Q=xy^2=2(2)=4