Show that the Lagrange equations for (x, y) = 2x + y subject to the constraint g(x,

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Show that the Lagrange equations for ƒ(x, y) = 2x + y subject to the constraint g(x, y) = x² − y² = 1 have a solution but that f has no min or max on the constraint curve. Does this contradict Theorem 1?

THEOREM 1 Lagrange Multipliers Assume that f(x, y) and g(x, y) are differen- tiable functions. If f(x, y) has

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 16, 2024 09:02 AM

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Show that the Lagrange equations for (x, y) = 2x + y subject to the constraint g(x,

Question:

THEOREM 1 Lagrange Multipliers Assume that f(x, y) and g(x, y) are differen- tiable functions. If f(x, y) has a local minimum or a local maximum on the constraint curve g(x, y) = 0 at P = (a, b), and if Vgp #0, then there is a scalar such that Vfp = Vgp

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or and hence Using the methods of Lagrange we can write Vf Vg and see 2 1 2x 2y 2 21x Ev...View the full answer

Calculus

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