Finding the point on y=x² closest to (2,1) using Lagrange multipliers

[fnord]

Hi! Probably quite easy for you guys (Im not even sure I am in the right thread).

The assignment is in constrained optimization, and we're supposed to use lagrange to find the point on the parabola y=x^2 which is closes to (2, 1). I've been trying for a while and can't seem to find the right answer, so I hope you can help me.

Cheers!

Updated: I am putting in my "progress":

I've used lagrange, with the restriction (y-x^2), and objective function (x-2)^2 + (y-1)^2
Cutting the lambda I get:

2(x-2)=2(y-1)(-2x)

y-x^2=0

And from there I don't know where to go. :(

 

[HallsofIvy]

You're supposed to? You mean this is work for a class? Then it should have been posted in the "homework and classwork" section. I will move it. Also, you are required to show what you have done yourself so we will know what hints you need. Since you say you have "been trying for a while", you should have a lot to show us.

 

[fnord]

Ah, thanks. It is my first post as you see, and its not homework, but it is in a textbook. I am starting math again by myself and its hard when you don't have anyone to ask. (Im working with political sciences;)

 

[lugita15]

Ah, thanks. It is my first post as you see, and its not homework, but it is in a textbook.

Just so you know, for the purposes of Physics Forums it doesn't matter whether it's actual homework. As long as it's a homework-style question, you have to do things like show the work you've already done in order to get help.