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Math Help - Global min and max multivariable

  1. #1
    Junior Member
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    Global min and max multivariable

    Can someone help me get the Global min and max. I know how to find the critical points but I'm not sure how to tell if its the global max and min. Here is the problem:



    F(x,y)=4e^-(4x^2+8y^2), 4x^2+8y^2 < or = to 3 ( just in case the above picture doesnt paste right once thread is posted)

    Thanks
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  2. #2
    MHF Contributor

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    The max and min may occur at a critical point inside the set, or on the boundary of a set. Here, that is particularly easy because on the boundary, 4x^2+ 8y^2= 3 so your function is just f(x, y)= 4e^{-3}, a constant.

    Evaluate the function at all critical points inside the set and on the boundary and see which are smallest and largest!
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