I'm studying for my calc II exam, and I recently discovered how one can solve max/min problems with constrains using AM-GM inequalities instead of lagrange multipliers. Seeing as this is way more elegant, I'd like to learn more about it.
Could someone help me find the maximum and minimum value of $3+2xy$ subject to the constraint $x^2+y^2=1$. I've already solved it using lagrange multipliers, but I'd like to see how it can be solved using AM-GM aswell.
(I've only looked at the very basics of AM-GM so far, but I couldn't find much online about how to utilize the inequalities when you have a constraint. Is this worth learning before my exam?)