Explanation Given information: The function f ( x , y ) = 3 x − 6 y − 8 and the domain is | x | + | y | ≤ − 3 Concept Used: A linear function f ( x , y ) = a x + b y + c has no critical point, therefore the global maximum and minimum value of must occur on the boundary of a bounded domain Calculation: As f ( x , y ) = 3 x − 6 y − 8 is linear function thus it has no critical point, therefore the global maximum and minimum value of must occur on the boundary of domain | x | + | y | ≤ − 3 First simplify the domain, as | x | + | y | ≤ − 3 is a rhombus with it’s edges on x -axes and y -axes, edges of (corner points) | x | + | y | ≤ − 3 are ( − 3 , 0 ) , ( 3 , 0 ) , ( 0 , 3 ) , ( 0 , − 3 ) , checking value of function

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Chapter 14.7, Problem 36E

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Find the global maximum and global minimum value of f(x,y)=3x−6y−8 on the bounded domain |x|+|y|≤−3 and indicate where they occur

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Chapter 14.7, Problem 35E

Chapter 14.7, Problem 37E

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Chapter 14 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

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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Find the global maximum and global minimum value of f ( x , y ) = 3 x − 6 y − 8 on the bounded domain | x | + | y | ≤ − 3 and indicate where they occur

Solution Summary: The author explains that the global maximum and minimum value of f(x,y)=3x-6y-8 must occur on the boundary of a bounded domain.

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Find the global maximum and global minimum value of f(x,y)=3x−6y−8 on the bounded domain |x|+|y|≤−3 and indicate where they occur

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Chapter 14 Solutions