Global Maximum and Global Minimum
Consider the following function:
f(x,y) = xy on the set S = {x^2 +4y^2 ? 1}.
a) Explain by applying a relevant theorem why f(x,y) has a
global maximum and a global minimum in the set S.
b) Find the critical of f in the interior of the set S.
c) Use the method of Lagrange multipliers to find the minima
and maxima of f on the boundary of S given by x^2 + 4y^2 =1.
d) Find the global maximum and the global minimum of f.
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