Ok, I'm having a problem understanding a question about Lagrange Multipliers.
Given the function
f(
x,
y) = 16 −
x2 −
y2 and the constraint (
x − 1)
2 + (
y − 1)
2 = 4, find the maximum and minimum.
I've reduced it to the system:
- -2x = λ∙2x
- -2y = λ∙2y
- (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?