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Math Help - Absolute Extrema

  1. #1
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    Exclamation 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\}
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  2. #2
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    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.
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  3. #3
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    Quote Originally Posted by TwistedOne151 View Post
    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
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  4. #4
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    What did you get for the partial derivatives, then?

    --Kevin C.
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  5. #5
    MHF Contributor Mathstud28's Avatar
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    You are going to need to apply the method of Lagrange Multipliers here.

    Lagrange multipliers - Wikipedia, the free encyclopedia

    If you encounter any problems report back and we will help.
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