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Unformatted text preview: a Method of Lagrange multipliers Suppose we wish to ﬁnd the maximum and minimum values of a function f ( x , y ) along a curve speciﬁed by g ( x , y ) = k . We must ﬁnd where ∇ f is parallel to ∇ g . This occurs when ∇ f = λ ∇ g . The solution to the optimization problem is the solution to the following set of equations ∇ f = λ ∇ g g ( x , y ) = k Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr a Class exercise Find the maximum and minimum values of the function f ( x , y ) = 4 x + 6 y subject to the constraint x 2 + y 2 = 13. Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr a Class exercise Find the maximum and minimum values of the function f ( x , y ) = 4 x + 6 y subject to the constraint x 2 + y 2 = 13. Answer: f (2 , 3) = 26 is the maximum. f (2 , 3) =26 is the minimum. Lecture 10 1 2 : Maximum and Minimum Values Subject to Contr a...
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 Spring '03
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 Multivariable Calculus, Optimization, minimum values, Minimum Values Subject

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