Explanation Given Information: The provided function is f ( x , y ) = 4 x y subject to x 2 + y 2 = 8 . Formula used: The steps for a relative extrema of a function f ( x , y , ... ) subject to the constraint g ( x , y , ... ) = 0 . 1. Construct the Lagrangian function, L ( x , y , ... ) = f ( x , y , .... ) − λ g ( x , y , .... ) , Where λ a new unknown is called a Lagrange multiplier. 2. The relative extrema occur at the critical points of L ( x , y , .... ) . Now, set all the partial derivatives of L ( x , y , ... ) equal to zero and solve the resulting system with the provided constraint equation g ( x , y , ... ) = 0 for the unknowns x , y , ... and λ . Calculation: Start by rewriting the problem with the constraint in the form g ( x , y ) = 0 . Maximize f ( x , y ) = 4 x y subject to x 2 + y 2 = 8 . Here, g ( x , y ) = x 2 + y 2 − 8 And, the Lagrangian function is, L ( x , y ) = f ( x , y ) − λ g ( x , y ) = 4 x y − λ ( x 2 + y 2 − 8 ) The system of equations needed to be solved are, L x = 0 , 4 y − 2 λ x = 0 And, L y = 0 , 4 x − 2 λ y = 0 Also, g ( x

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

7th Edition

ISBN: 9781337291293

Author: Waner, Stefan; Costenoble, Steven

Publisher: Brooks Cole

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Chapter 8.4, Problem 9E

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To calculate: The maximum value of f(x,y)=4xy subject to x2+y2=8.

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Chapter 8.4, Problem 8E

Chapter 8.4, Problem 10E

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Chapter 8 Solutions

Student Solutions Manual for Waner/Costenoble's Applied Calculus, 7th

Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 14, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 6E Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - For each function in Exercises 5-8, evaluate (a)...Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

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The maximum value of f ( x , y ) = 4 x y subject to x 2 + y 2 = 8 .

Solution Summary: The author explains how to calculate the maximum value of f(x,y)=4xy subject to a constraint.

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To calculate: The maximum value of f(x,y)=4xy subject to x2+y2=8.

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Chapter 8 Solutions