For each of the following, use Lagrange multipliers to find all extrema of f subject to the
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a) f(x, y) = x + y2 and x2 + y2 = 4
b) f(x, y) = x2 - 4xy + 4y2 and x2 + y2 = 1
c) f(x, y, z) = xy, x2 + y2 + z2 = 1 and x + y + z = 0
d) f(x, y, z, w) = 3x + y + w, 3x2 + y + 4z3 = 1 and -x3 + 3z4 + w = 0
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a The Lagrange equations are 1 2x and 2y 2y If y 0 then the constraint implies x 2 If y 0 then 1 so ...View the full answer
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