Explanation Given information: f ( x , y ) = x 2 − x y + y 2 , P = ( − 1 , 4 ) Calculation: Since the gradient of function is denoted by ∇ f = 〈 ∂ f ∂ x , ∂ f ∂ y 〉 The given equation f ( x , y ) = x 2 − x y + y 2 , Differentiating f with respect to x we get, ∂ f ∂ x = ∂ ∂ x x 2 − x y + y 2 ⇒ ∂ f ∂ x = ∂ ∂ x x 2 − ∂ ∂ x x y + ∂ ∂ x y 2 ⇒ ∂ f ∂ x = 2 x − y + 0 = 2 x − y Differentiating f with respect to y we get, ∂ f ∂ y = ∂ ∂ y x 2 − x y + y 2 ⇒ ∂ f ∂ y = ∂ ∂

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

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ISBN: 9781319057664

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.5, Problem 34E

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the direction in which f has maximum rate of increase from P, and give the rate of change in that direction.

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Chapter 14.5, Problem 33E

Chapter 14.5, Problem 35E

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Chapter 14 Solutions

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

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 direction in which f has maximum rate of increase from P , and give the rate of change in that direction.

Solution Summary: The author explains how to find the direction in which f has maximum rate of increase from P.

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Tofind:

the direction in which f has maximum rate of increase from P, and give the rate of change in that direction.

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Chapter 14 Solutions

Tofind: the direction in which f has maximum rate of increase from P , and give the rate of change in that direction.

Solution Summary: The author explains how to find the direction in which f has maximum rate of increase from P.

Videos

Tofind: the direction in which f has maximum rate of increase from P, and give the rate of change in that direction.

Want to see the full answer?

Chapter 14 Solutions

Tofind:

the direction in which f has maximum rate of increase from P, and give the rate of change in that direction.