1. ## Absolute Extrema

Find the absolute extrema of $f(x,y) = 2xy + \sqrt{1-x^2-y^2}$ on the region $D = \{(x,y) \in \Re^2 : x^2+y^2 \leq 1\}$

2. The absolute extrema of a function on a closed region are either local extrema (where the gradient is zero), or on the boundary of the region. Check for local extrema in the region, and check the values on the boundary.

--Kevin C.

3. Originally Posted by TwistedOne151
The absolute extrema of a function on a closed region are either local extrema (where the gradient is zero), or on the boundary of the region. Check for local extrema in the region, and check the values on the boundary.

--Kevin C.
The thing is... I can't find the critical points.. I found the partial derivatives and set them equal to zero.. now what? can anyone solve this for me?? thanks

4. What did you get for the partial derivatives, then?

--Kevin C.

5. You are going to need to apply the method of Lagrange Multipliers here.

Lagrange multipliers - Wikipedia, the free encyclopedia

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