Explanation Given information: The f ( x , y ) = 2 x 2 − 4 x y 2 Concept used: The equation of the tangent plane to the grpah of f ( x , y ) = 2 x 2 − 4 x y 2 at ( a , b ) is z = f ( a , b ) + f x ( a , b ) ( x − a ) + f y ( a , b ) ( y − b ) Calculation: The polynomial, f ( x , y ) = 2 x 2 − 4 x y 2 So f ( x , y ) at ( − 1 , 2 ) f ( − 1 , 2 ) = 2 ( − 1 ) 2 − 4 ( − 1 ) ( 2 ) 2 = 2 + 16 = 18 Differentiating both sides with respect to x , we get, f x ( x , y ) = 4 x − 4 y 2 So f x ( x , y ) at ( − 1 , 2 ) f x ( − 1 , 2 ) = 4 ( − 1 ) − 4 ( 2 ) 2 ⇒ f x ( − 1 , 2 ) = − 4 − 4 ( 4 ) ⇒ f x ( − 1 , 2 ) = − 4 − 16 = − 20 Now we will differentiate f ( x , y )

4th Edition

ISBN: 9781319279813

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.4, Problem 1E

To determine

Tofind:

an equation of the tangent plane to the graph of f(x,y)=2x2−4xy2 at (−1,2).

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Chapter 14.4, Problem 6PQ

Chapter 14.4, Problem 2E

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Chapter 14 Solutions

CALCULUS:EARLY TRANS.-SAPLINGPLUS

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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Tofind: an equation of the tangent plane to the graph of f ( x , y ) = 2 x 2 − 4 x y 2 at ( − 1 , 2 ) .

Solution Summary: The author calculates the equation of the tangent plane to the graph of f(x,y) = 2x2-4x

Videos

Tofind:

an equation of the tangent plane to the graph of f(x,y)=2x2−4xy2 at (−1,2).

Want to see the full answer?

Chapter 14 Solutions

Tofind: an equation of the tangent plane to the graph of f ( x , y ) = 2 x 2 − 4 x y 2 at ( − 1 , 2 ) .

Solution Summary: The author calculates the equation of the tangent plane to the graph of f(x,y) = 2x2-4x

Videos

Tofind: an equation of the tangent plane to the graph of f(x,y)=2x2−4xy2 at (−1,2).

Want to see the full answer?

Chapter 14 Solutions

Tofind:

an equation of the tangent plane to the graph of f(x,y)=2x2−4xy2 at (−1,2).