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## Homework Statement

Find the maximum and minimum values of 2x

^{2}+ y

^{2}on the curve x

^{2}+ y

^{2}- 4x = 5 by the method of Lagrange Multipliers.

## Homework Equations

I will express my Lagrange multipliers as λ.

## The Attempt at a Solution

Okay so we want the max min of f(x,y) = 2x

^{2}+ y

^{2}given the constraint that : x

^{2}+ y

^{2}- 4x = 5.

So the first thing I want to note is I can express my constraint in terms of a function g = x

^{2}+ y

^{2}- 4x - 5. I believe that the max or min will occur somewhere on my constraint which happens to be a boundary. Since I don't have any interior to examine, I don't even need to know critical points of f. So the first thing I should do is form my Lagrange equation :

F = f + λg = 2x

^{2}+ y

^{2}+ λ(x

^{2}+ y

^{2}- 4x - 5)

Now I should take the derivative of big F with respect to x, y and then λ and form a system of equations right?

Is this good so far? ( First time trying one of these myself ).