Explanation Given information: f ( x , y , z ) = x y z , P = ( 1 , − 1 , 3 ) Calculation: Since the gradient of function is denoted by ∇ f = 〈 ∂ f ∂ x , ∂ f ∂ y , ∂ f ∂ y 〉 The given equation f ( x , y , z ) = x y z , Differentiating f with respect to x we get, ∂ f ∂ x = ∂ ∂ x ( x y z ) ⇒ ∂ f ∂ x = y z ∂ ∂ x x ⇒ ∂ f ∂ x = y z Differentiating f with respect to y we get, ∂ f ∂ y = ∂ ∂ y x y z ⇒ ∂ f ∂ y = x z ∂ ∂ y y = x z Differentiating f with respect to z we get, ∂ f ∂ z = ∂ ∂ z x y z ⇒ ∂ f ∂ z = x y ∂ ∂ z 1 z = x y

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Author: Rogawski

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Chapter 14.5, Problem 35E

To determine

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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 34E

Chapter 14.5, Problem 36E

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Chapter 14 Solutions

CALCULUS: EARLY TRANS 4TH ED W/ ACCESS

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 determine 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.

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.

Solution Summary: The author explains how to determine 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.