Explanation Given information: ∇ f p = ( 2 , − 4 , 4 ) , v = ( 2 , 1 , 3 ) Calculation: We will find the unit vector along v = 〈 2 , 1 , 3 〉 Hence e ^ = v | v | = 〈 2 , 1 , 3 〉 2 2 + 1 2 + ( 3 ) 2 = 1 14 〈 2 , 1 , 3 〉 The directional derivative in the direction of v at the given point P is given by, D v f ( 2 , 1 , 3 ) = ∇ f ( 2 , 1 , 3 )

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Chapter 14.5, Problem 37E

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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 36E

Chapter 14.5, Problem 38E

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Chapter 14 Solutions

CALCULUS 4E (HC) W/ ACHIEVE 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 calculates the directional derivative in the direction of v at the given point 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 calculates the directional derivative in the direction of v at the given point 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.