Take home exam problem. Someone want to tell me if I'm missing something with this Lagrange multiplier problem?
Problem: Find the maximum and minimum values of f(x,y)=xy on the curve (x+2)^2 + y^2 =1
This is what I've done-
gradient of f=(y,x)
gradient of g=(2x+4,2y)
According to Lagrange: gradient f = lambda*(gradient g)
So we have the following equations.
(x+2)^2 + y^2 =1
That's 3 equations and 3 unknowns but I can't seem to find a solution. I feel like I'm missing something really stupid. Or my brain is hitting a wall to solve those equations. Can someone help?