Ok, I’m having a problem understanding a question about Lagrange Multipliers.

Given the function *f*(*x*, *y*) = 16 − *x*2 − *y*2 and the constraint (*x* − 1)2 + (*y* − 1)2 = 4, find the maximum and minimum.

I’ve reduced it to the system:

- -2
*x*

= λ∙2*x* - -2
*y*

= λ∙2*y* - (
*x*

− 1)2 + (*y*− 1)2 = 4

There are a few ways to solve this:

- Assume λ = -1, which gets you nowhere
- Assume
*x*

= 0, for which*y*= 1 ± √3 - Assume
*y*

= 0, for which*x*= 1 ± √3

I know that the real answer is when *x* = *y*, but I can’t get that going forwards.

Anyone have suggestions as to how to approach it?