Explanation Given information: f ( x , y ) = ( x + 1 ) y 2 ,tangent plane is horizontal. Calculation: The tangent plane to f ( x , y ) = ( x + 1 ) y 2 is horizontal at the points where ∂ f ∂ x = 0 and ∂ f ∂ y = 0 . Consider, f ( x , y ) = ( x + 1 ) y 2 Differentiating f ( x , y ) with respect to x we get, ∂ f ∂ x = ∂ ∂ x ( x + 1 ) y 2 = ∂ ∂ x ( x y 2 + y 2 ) ⇒ ∂ f ∂ x = ∂ ∂ x x y 2 + ∂ ∂ x y 2 ⇒ ∂ f ∂ x = y 2 ( 1 ) + ( 0 ) ⇒ ∂ f ∂ x = y 2 So, for ∂ f ∂ x = 0 we get, y 2 = 0 y = 0 ..

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Author: Jon Rogawski, Colin Adams, Robert Franzosa

Publisher: W. H. Freeman

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Chapter 14.4, Problem 14E

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the points on the graph of f(x,y)=(x+1)y2 where the tangent plane is horizontal.

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Chapter 14.4, Problem 13E

Chapter 14.4, Problem 15E

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Chapter 14 Solutions

Calculus: Early Transcendentals

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: the points on the graph of f ( x , y ) = ( x + 1 ) y 2 where the tangent plane is horizontal.

Solution Summary: The author calculates that the tangent plane is horizontal on the graph of f(x,y) = left.

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Tofind:

the points on the graph of f(x,y)=(x+1)y2 where the tangent plane is horizontal.

Want to see the full answer?

Chapter 14 Solutions

Tofind: the points on the graph of f ( x , y ) = ( x + 1 ) y 2 where the tangent plane is horizontal.

Solution Summary: The author calculates that the tangent plane is horizontal on the graph of f(x,y) = left.

Videos

Tofind: the points on the graph of f(x,y)=(x+1)y2 where the tangent plane is horizontal.

Want to see the full answer?

Chapter 14 Solutions

Tofind:

the points on the graph of f(x,y)=(x+1)y2 where the tangent plane is horizontal.