- #1
MrCreamer
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Homework Statement
Find the extrema of f(x, y) = x2−2xy+ 2y2, subject to the
constraint x2 +y2 = 1.
Homework Equations
∇f(x,y) = λg(x,y)
The Attempt at a Solution
This is the work I have thus far:
Letting g(x,y) = x2+y2-1,
We obtain the following three equations from the Lagrange Multiplier equation:
2x-2y = 2λx
4y-2x = 2λy
x2+y2-1=0
I know that x and y cannot both be zero due to the constraint equation.
If x = 0:
4y = 2λy
--> λ = 2
If y = 0:
2x = 2λx
--> λ = 1
I have no idea what else to do