Explanation Given: The given function is f ( x , y ) = x + y . The constraint is g ( x , y ) = x 2 + y 2 − 1 . Formula used: The Lagrange function is, L ( x , y ) = f ( x , y ) − λ g ( x , y ) Calculation: Consider the Lagrange function for the given function with multiplier λ . L ( x , y ) = x + y − λ ( x 2 + y 2 − 1 ) L ( x , y ) = x + y − λ x 2 − λ y 2 + λ The first order partial derivatives of L are, L x = 1 − 2 λ x L y = 1 − 2 λ y The system of equations is, L x = 0 ; L y = 0 ; g ( x , y ) = 0 The above system of equations gives the following results. 1 − 2 λ x = 0 ⇒ 1 = 2 λ x ⇒ x = 1 2 λ 1 − 2 λ y = 0 ⇒ 1 = 2 λ y ⇒ y = 1 2 λ x 2 + y 2 − 1 = 0 Substitute the values of x and y in x 2 + y 2 − 1 = 0

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Chapter 8.6, Problem 1P

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The maximum and minimum value of the function f(x,y)=x+y.

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Chapter 8.5, Problem 32P

Chapter 8.6, Problem 2P

Chapter 8 Solutions

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The maximum and minimum value of the function f ( x , y ) = x + y .

Solution Summary: The author calculates the maximum and minimum value of the function f(x,y)=x+y. The system of equations gives the following results.

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To find:

The maximum and minimum value of the function f(x,y)=x+y.

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Chapter 8 Solutions

The maximum and minimum value of the function f ( x , y ) = x + y .

Solution Summary: The author calculates the maximum and minimum value of the function f(x,y)=x+y. The system of equations gives the following results.

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To find: The maximum and minimum value of the function f(x,y)=x+y.

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Chapter 8 Solutions

To find:

The maximum and minimum value of the function f(x,y)=x+y.