Find the maximum and minimum values of 2x2 + y2 on the curve x2 + y2 - 4x = 5 by the method of Lagrange Multipliers.
I will express my Lagrange multipliers as λ.
The Attempt at a Solution
Okay so we want the max min of f(x,y) = 2x2 + y2 given the constraint that : x2 + y2 - 4x = 5.
So the first thing I want to note is I can express my constraint in terms of a function g = x2 + y2 - 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 = 2x2 + y2 + λ(x2 + y2 - 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 ).