Find all absolute minimums and maximums of the function f x

Find all absolute minimums and maximums of the function f (x, y) = x2 + 2xy + y2 over the domain D = {(x, y) : x2 + y2 ? 8} (i.e. the closed disk of radius ?8 centered at (0, 0)). Note: this is a continuous function defined on a closed and bounded domain, so by the Extreme Value Theorem there must be at least one point in the domain which is an absolute maximum and a point in the domain which is an absolute minimum. Hint: You can use Langrange multipliers to check for the candidate extreme values on the boundary of the domain, and there may be many critical points in the interior of D.