# Math Help - find Extreme values of f(x,y) , subject to g(x,y)

1. ## find Extreme values of f(x,y) , subject to g(x,y)

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 fx = λgx => 2(x-1) = (2x)λ

and fy= λgy => 2(y+2) = (2y)λ

but λ is meant to be a constant.

2. ## Re: find Extreme values of f(x,y) , subject to g(x,y)

With those two equations and the constraint, you have three equations and three unknowns.

3. ## Re: find Extreme values of f(x,y) , subject to g(x,y)

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?

4. ## Re: find Extreme values of f(x,y) , subject to g(x,y)

No,there are only two points, not four. You have the earlier equation $y=-2x.$

5. ## Re: find Extreme values of f(x,y) , subject to g(x,y)

oh right, so (-1, 2) and (1,-2)?