Lagrange multipliers

[tribal verge]

I pretty much understand how to do these problems but the issue I am having is when I set Fx and Fy to 0 and I get a fraction with lambda for both, and I am not getting x and y at the end but rather a function

Fx would be -1-4xlambda=0 and Fy is -1-2ylambda=0 but settign them to 0 gives me 1/2lmabda and 1/4lambda which I feel is incorrect, unless it is not but plugging into Flambda I do not get x and y

[steep matrix]

@tribal verge Pluging those in the constraint equation and solving you get the values of lamda which then you substitute to the x and y you found

[idle jackal]

Let's see.
L(x, y, λ) = -x - y - (2x^2 + y^2 - 54)λ
We take all partial derivatives to be zero.
∂L/∂x = -1 - 4xλ = 0
∂L/∂y = -1 - 2yλ = 0
∂L/∂λ = 2x^2 + y^2 - 54 = 0
From the first equation:
x = -1/(4λ)
From the second equation:
y = -1/(2λ)
Then just substitute that into the third equation. The rest is easy.

[tribal verge]

ahh I see, somehow I was doing my math wrong when plugging in x and y into the third equation because I was getting a function instead but now I see its 1/12 and f and x = 3 and 6, correct? unless its -3 and -6

[steep matrix]

@tribal verge unless you read first word of the question

@tribal verge you get two values of lamda, what do you think those correspond to?

[idle jackal]

That's one of the values.
You should get both points, then check which one of them is the minimum and which one is the maximum.

[tribal verge]

ty! I was over complicating the problem but now I believe i got the right answer of f(3,6) being -9 as I have to assume x and y are positive so -1/12 was what i plugged into lambda in x and y

[devout grove]

@tribal verge has given 1 rep to @idle jackal