a. Explanation Given: The function f ( x , y ) = x 2 + y 2 x y , a point P 0 ( 1 , − 1 , − 2 ) and the direction parallel to the x z - plane . Concept Used: For a function that defines a surface z = f ( x , y ) differentiated at a point ( x 0 , y 0 ) . The equation of the tangent plane to the surface z = f ( x , y ) at a point ( x 0 , y 0 ) is given by z = f ( x 0 , y 0 ) + f x ( x 0 , y 0 ) ( x − x 0 ) + f y ( x 0 , y 0 ) ( y − y 0 ) Calculation: For the givensurface f ( x , y ) = x 2 + y 2 x y and a point P 0 ( 1 , − 1 , − 2 ) Consider f ( x , y ) = x 2 + y 2 x y f ( x , y ) = x 2 + y 2 x y = x 2 x y + y 2 x y = x y + y x Calculating the partial derivatives f x ( x , y ) = 1 y − y x 2 and f y ( x , y ) = − x y 2 + 1 x At point P 0 ( 1 , − 1 , − b. To determine To find: The slope of the tangent line to the graph of f ( x , y ) = x 2 + y 2 x y at point P 0 ( 1 , − 1 , − 2 ) in the direction parallel to the y z - plane .

Student's Solution and Survival Manual for Calculus

7th Edition

ISBN: 9781524934040

Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J

Publisher: Kendall Hunt Publishing

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Chapter 11.3, Problem 30PS

To determine

To find:The slope of the tangent line to the graph of f(x,y)=x2+y2xy at point P0(1,−1,−2) in the direction parallel to the xz-plane .

To determine

To find:The slope of the tangent line to the graph of f(x,y)=x2+y2xy at point P0(1,−1,−2) in the direction parallel to the yz-plane .

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Chapter 11.3, Problem 29PS

Chapter 11.3, Problem 31PS

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Chapter 11 Solutions

Student's Solution and Survival Manual for Calculus

Ch. 11.1 - Prob. 1PS Ch. 11.1 - Prob. 2PS Ch. 11.1 - Prob. 3PS Ch. 11.1 - Prob. 4PS Ch. 11.1 - Prob. 5PS Ch. 11.1 - Prob. 6PS Ch. 11.1 - Prob. 7PS Ch. 11.1 - Prob. 8PS Ch. 11.1 - Prob. 9PS Ch. 11.1 - Prob. 10PS

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The slope of the tangent line to the graph of f ( x , y ) = x 2 + y 2 x y at point P 0 ( 1 , − 1 , − 2 ) in the direction parallel to the x z - plane .

Solution Summary: The author calculates the slope of the tangent line to the graph of f(x,y)=x2+y

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To find:The slope of the tangent line to the graph of f(x,y)=x2+y2xy at point P0(1,−1,−2) in the direction parallel to the xz-plane .

To find:The slope of the tangent line to the graph of f(x,y)=x2+y2xy at point P0(1,−1,−2) in the direction parallel to the yz-plane .

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Chapter 11 Solutions