Explanation Approach: To find f x ( x , y ) , differentiate f ( x , y ) with respect to x by holding y , f x ( x , y ) = ∂ ∂ x f ( x , y ) To find f y ( x , y ) , differentiate f ( x , y ) with respect to y by holding x , f y ( x , y ) = ∂ ∂ y f ( x , y ) Calculation: Consider the given function, f ( x , y ) = 50 + 4 x − 5 y + x 2 + y 2 + x y To find f x ( x , y ) , differentiate f ( x , y ) with respect to x by holding y , f x ( x , y ) = ∂ ∂ x ( 50 + 4 x − 5 y + x 2 + y 2 + x y ) = ∂ ∂ x ( 50 ) + 4 ∂ ∂ x ( x ) − 5 ∂ ∂ x ( y ) + ∂ ∂ x ( x 2 ) + ∂ ∂ x ( y 2 ) + ∂ ∂ x ( x y ) = 4 + 2 x + y Thus, f x ( x , y ) = 4 + 2 x + y . Substitute f x ( x , y ) = 0 in the function f x ( x , y ) = 4 + 2 x + y , 2 x + y = − 4... ( 1 ) To find f y ( x , y ) , differentiate f ( x , y ) with respect to y by holding x ,

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ISBN: 9780321964458

Author: Lial

Publisher: PEARSON EDUCATION (COLLEGE)

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Chapter 9.2, Problem 38E

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The values of x and y such that fx(x,y)=0 and fy(x,y)=0 for the function f(x,y)=50+4x−5y+x2+y2+xy.

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Chapter 9.2, Problem 37E

Chapter 9.2, Problem 39E

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Chapter 9 Solutions

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The values of x and y such that f x ( x , y ) = 0 and f y ( x , y ) = 0 for the function f ( x , y ) = 50 + 4 x − 5 y + x 2 + y 2 + x y .

Solution Summary: The author explains how to find x and y for the function f(x,y).

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To find:

The values of x and y such that fx(x,y)=0 and fy(x,y)=0 for the function f(x,y)=50+4x−5y+x2+y2+xy.

Want to see the full answer?

Chapter 9 Solutions

The values of x and y such that f x ( x , y ) = 0 and f y ( x , y ) = 0 for the function f ( x , y ) = 50 + 4 x − 5 y + x 2 + y 2 + x y .

Solution Summary: The author explains how to find x and y for the function f(x,y).

Videos

To find: The values of x and y such that fx(x,y)=0 and fy(x,y)=0 for the function f(x,y)=50+4x−5y+x2+y2+xy.

Want to see the full answer?

Chapter 9 Solutions

To find:

The values of x and y such that fx(x,y)=0 and fy(x,y)=0 for the function f(x,y)=50+4x−5y+x2+y2+xy.