(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant equations

f=(x-1)^2 + (y-1)^2

g=x^2+y^2=45

gradf(x,y)=lambda*gradg(x,y)

3. 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

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# Homework Help: Lagrange Multipliers HELP PLEASE

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