Let P1; P2; :::Pk be points that satisfy the Lagrange multiplier condition for a function f(x; y) subject to the constraint g(x; y) =0. Which of the following is true?

A)One of the points is a maximum and

one of the points is a minimum of f(x; y)

subject to the constraint g(x; y) = 0.

B)If the constraint curve g(x; y) is bounded,

then f(x; y) has a max at one of the

points and a min at another point Pi

C. It is possible for f(x; y) to neither have

a max or min at one of the points Pi

.

D. (b) and (c) are true

E. none of the above

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