Extreme values of f(x,y) = (x-1)^2 + (y+2)^2
on the circle x^2 + y^2 = 5
I thought it was done by f_{x} = λg_{x} => 2(x-1) = (2x)λ
and f_{y}= λg_{y} => 2(y+2) = (2y)λ
but λ is meant to be a constant.
ah yep.
so from first one λ = 1 - 1/x
sub that into the second one gives y = -2x
sub that into the constraint gives 5x^2 = 5 => x^2 = +1 or -1
for x=-1
y= +2 or -2
and for x= 1
y= +2 or -2.
so extreme points at (-1,-2), (-1, 2), (1,-2), (1, 2). Correct?