Find the absolute extrema of $\displaystyle f(x,y) = 2xy + \sqrt{1-x^2-y^2}$ on the region $\displaystyle D = \{(x,y) \in \Re^2 : x^2+y^2 \leq 1\}$
You are going to need to apply the method of Lagrange Multipliers here.
Lagrange multipliers - Wikipedia, the free encyclopedia
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