Lagrange Multipliers

In fairly simple words, the method of Lagrange multipliers is exactly what you have said: find the turning points given a set of constraints. So in the first step, you introduce lambda(xy-1) into your function that leaves it unchanged because it equals to 0, and you WANT the function to be governed by this fixed set of x-y values that it can only take. You don't actually need to find lambda, because it's a dummy variable that you introduce with the aim of removing it later without finding out what it is i.e. its an auxillary function.

Just like that. Lambda comes in useful later at some other points, but let someone more versed in this come and give a better explanation. I'm late for lecture.

Hadriel