Let (a) Show that there is a unique point P = (a, b) on g(x, y) =

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Let f(x,y) = x+xy + y, g(x, y) = x xy + y - 3

(a) Show that there is a unique point P = (a, b) on g(x, y) = 1 where ∇ƒP = λ∇gP for some scalar λ.
(b) Refer to Figure 13 to determine whether ƒ(P) is a local minimum or a local maximum of ƒ subject to the constraint.
(c) Does Figure 13 suggest that ƒ(P) is a global extremum subject to the constraint?

2 y 0+ -2 -2 -1 0 -3 0 P -5 5 3 1 2

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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