Question

Optimization inside a region:
Find the extrem values of f(x,y)=x^2+2y^2-2x+3
subject to the constraint x^2+y^2 greater than or equal to 0

Answer 1

I believe i know how to get the points on the circle, using lagrange multiplier, but what about for points inside the circle? Do i just use partial deriavtives? and if so does the constraint play a role in that?

Answer 2

http://math.stackexchange.com/questions/49473/lagrange-multipliers-with-inequality-constraints
Check the answer by mixedmath. That was a rectangular region, but it's easily taken elsewhere.