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?
Any advice is welcome.
Thank you for your time.