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I have posted a link there to this thread so the OP can see my work.Find the extreme values of f, on a given region? Using LaGrange multipliers?

Find the extreme values of f(x,y) = 6x^2+3y^2-36x-1, on the region described by x^2+y^2 <=36.

I'm pretty sure you have to use LaGrange multipliers. I ended up with lamba=0, x=3, y= +/-sqrt(27) which doesn't seem right.

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Actually I just got the absolute minimum value by taking partial derivatives of f with respect to x and y. How do I get the absolute max?