Find the stationary points of the function $f(x) = x^2 + y^2$ subjected to the constraint $$ x^2 + y^2 + 2x - 2y +1 =0.$$
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what did you try? – Gustave Oct 27 '21 at 21:53
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Please help with this. I have a problem with this – daniel marvin Oct 27 '21 at 21:54
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It would be best if you could tell us what you have tried so far to solve the problem. – Hilberto1 Oct 27 '21 at 22:00
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@danielmarvin It helps (both you and us) for us to know more about you, what you're learning, what you're comfortable with, what techniques you expect to see in a solution, etc. There's a couple of ways to approach this, and it's not going to help you to see a solution involving tools you don't have access to, or an ad hoc solution where you're expected to use some kind of general method. What course are you taking at the moment? What kinds of things have you been learning recently? The more we know, the better our answers can be. – Theo Bendit Oct 27 '21 at 22:03
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Tried using Lagrange multipliers. I have a problem with this particular question. Can someone help me please. I – daniel marvin Oct 27 '21 at 22:03
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1@danielmarvin Lagrange multipliers was what I was thinking of when I spoke about general methods. Another way you could tackle this is to observe that the constraint is equivalent to $(x + 1)^2 + (y - 1)^2 = 1$ (which I discovered by completing the square), then applying a parameterisation of the circle: $x = -1 + \cos(\theta)$ and $y = 1 + \sin(\theta)$, for $0 \le \theta \le 2\pi$. Plug these into the function, and you get a differentiable function of $\theta$. This will help get the stationary points. – Theo Bendit Oct 27 '21 at 22:43