Explanation Given Information: The function f ( x , y ) = x 2 + y 2 subject to the constraint 2 x + y = 10 . Formula Used: The extreme value of the function f ( x , y ) subject to the constraint g ( x , y ) can be obtained in the following steps: 1. Form a Lagrange function F ( x , y , λ ) = f ( x , y ) − λ g ( x , y ) . 2. Obtain the solutions for the system F x = 0 , F y = 0 , F λ = 0 as ( x , y , λ ) . 3. Then check whether the solution ( x , y ) is a maximum or a minimum value using test values from the constraints. Calculation: Consider the function, f ( x , y ) = x 2 + y 2 Rewrite the provided constraint as: 2 x + y = 10 2 x + y − 10 = 0 Now, form a new function F given by, F ( x , y , λ ) = x 2 + y 2 − λ ( 2 x + y − 10 ) Find F x , F λ and F y . For F x , x is treated as variable and y and λ are treated as constants and the equation is differentiated. F x = 2 x − 2 λ ….. ( 1 ) For F y , y is treated as variable and x and λ are treated as constants and the equation is differentiated. F y = 2 y − λ ….. ( 2 ) For F λ , λ is treated as variable and x and y are treated as constants and the equation is differentiated

Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

11th Edition

ISBN: 9780133862386

Author: Marvin L. Bittinger, David J. Ellenbogen, Scott J. Surgent

Publisher: PEARSON

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Chapter 6.5, Problem 3E

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To calculate: The extremum of f(x,y)=x2+y2 subject to the constraint 2x+y=10 and state whether it is a maximum or a minimum.

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Chapter 6.5, Problem 2E

Chapter 6.5, Problem 4E

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Calculus and Its Applications, Books a la Carte Plus MyLab Math Access Card Package (11th Edition)

Ch. 6.1 - Forf(x,y)=x23xy,find(0,2),f(2,3),andf(10,5).Ch. 6.1 - 2. . Ch. 6.1 - 3. . Ch. 6.1 - 4. . Ch. 6.1 - Forf(x,y)=Inx+y3,findf(e,2),f(e2,4),andf(e3,5).Ch. 6.1 - 6. . Ch. 6.1 - Forf(x,y,z)=x2y2+z2,findf(1,2,3)andf(2,1,3).Ch. 6.1 - 8. . Ch. 6.1 - In Exercises 9-14, determine the domain of each...Ch. 6.1 - In Exercises 9-14, determine the domain of each...

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The extremum of f ( x , y ) = x 2 + y 2 subject to the constraint 2 x + y = 10 and state whether it is a maximum or a minimum.

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To calculate: The extremum of f(x,y)=x2+y2 subject to the constraint 2x+y=10 and state whether it is a maximum or a minimum.

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