Hello,

I've been looking at finding extreme points of the following function

over the constraint

using Lagrange multipliers.

, where g is the equation of the constraint.

This means

Following that, I made

It's easy to see here that

or

Making either substitution into the equation

, after simplifying, it makes it equal to

. This implies that y= 0,1 or -1. Substituting these values into the constraint, I find that if y = 0, x = 1 & -1. If y = -1 and 1, values for x won't be real. So this gives me extreme points of (-1,0) and (1,0). Which, in turn, gives me an extreme value of 2 for both points.

My question is, am I right? Have I found the extreme points or have I missed some? Have I even got the right points?