Explanation Given information: f ( x , y ) = 3 x 3 − x y − y 2 ,tangent plane is horizontal. Calculation: The tangent plane to f ( x , y ) = 3 x 3 − x y − y 2 is horizontal at the points where ∂ f ∂ x = 0 and ∂ f ∂ y = 0 . Consider, f ( x , y ) = 3 x 3 − x y − y 2 Differentiating f ( x , y ) with respect to x we get, ∂ f ∂ x = ∂ ∂ x ( 3 x 3 − x y − y 2 ) ⇒ ∂ f ∂ x = ∂ ∂ x 3 x 3 − ∂ ∂ x x y − ∂ ∂ x y 2 ⇒ ∂ f ∂ x = 3 x 2 − ( y ) ( 1 ) − ( 0 ) ⇒ ∂ f ∂ x = 3 x 2 − y So, for ∂ f ∂ x = 0 we get, 3 x 2 = y ... ( 1 ) Differentiating f ( x , y ) with respect to y we get, ∂ f ∂ y = ∂ ∂ y ( 3 x 3 − x y − y 2 ) ⇒ ∂ f ∂ y = ∂ ∂ y 3 x 3 − ∂ ∂ y x y − ∂ ∂ y y 2 ⇒

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Author: Rogawski

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Chapter 14.4, Problem 13E

To determine

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the points on the graph of f(x,y)=3x3−xy−y2 where the tangent plane is horizontal.

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Chapter 14.4, Problem 12E

Chapter 14.4, Problem 14E

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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: the points on the graph of f ( x , y ) = 3 x 3 − x y − y 2 where the tangent plane is horizontal.

Solution Summary: The author calculates the tangent plane of f(x,y) = 3x3-xy-y

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Tofind:

the points on the graph of f(x,y)=3x3−xy−y2 where the tangent plane is horizontal.

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Chapter 14 Solutions

Tofind: the points on the graph of f ( x , y ) = 3 x 3 − x y − y 2 where the tangent plane is horizontal.

Solution Summary: The author calculates the tangent plane of f(x,y) = 3x3-xy-y

Videos

Tofind: the points on the graph of f(x,y)=3x3−xy−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)=3x3−xy−y2 where the tangent plane is horizontal.