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I had a lecture in an elementary Calculus course today, and the professor used a method for classifying critical points which I can't see in my book (Calculus, a complete course, by Adams). Basically he had the function

[itex]f(x,y)=x^2+2y^2-4x+4y.[/itex]

He found a critical point at (2,-1) - I have no problem understanding this part. However, he classified it as a local (and absolute) minimum because the function [itex]f(x,y)[/itex] would diverge for [itex]x^2+y^2\to \infty[/itex]. Where does this method come from and where can I read about it?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Classifying critical points

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