- #1
thanksie037
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Homework Statement
Find the maximum and minimum values of f = (x-1)^2 + (y-1)^2 on the boundary of the circle g = x^2 + y^2 = 45.
Homework Equations
f=(x-1)^2 + (y-1)^2
g=x^2+y^2=45
gradf(x,y)=lambda*gradg(x,y)
The Attempt at a Solution
gradf(x,y)=<2x-2,2y-4>
gradg(x,y)=<2x,2y>
(1) 2x-2=lambda*2x
(2) 2y-4=lambda*2y
(3)g=x^2+y^2=45
solving the system for critical points:
x = 1/(1-lambda) plug into g?
y = 2/(1-lambda) plug into g?
gives lambda = 1 - (1/x) and lambda = 1 - (2/y)
set lambda = lambda:
1 - (1/x) = 1 - (2/y)
(1/x) = (2/y)
y = 2*x
here's where I get lost, how do i plus this back in? I shouldn't have to know the sqrt(45) to solve this. HELP