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Example Find the dimensions of the rectangular box with an open top with largest volume if the total surface area is 216 cm².

Example Find the dimensions of the rectangular box with an open top with largest volume if the total surface area is 216 cm².

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Solve using Lagrange multiplier. Also use an auxiliary function such as the given below.

1. Create the auxiliary function F of four variables x, y, z, and A for which F(x, y, z, a) = f(x, y, z) + Ag(x, y, z) 2. Establish the system of equations obtained by setting the four first partial derivatives of F equal to zero. F(x, y, z, A) = 0 F,(x. y. z, A) = 0 |F,(x, y, z, A) = 0 F.(x, y, z, A) = 0
Transcribed Image Text:1. Create the auxiliary function F of four variables x, y, z, and A for which F(x, y, z, a) = f(x, y, z) + Ag(x, y, z) 2. Establish the system of equations obtained by setting the four first partial derivatives of F equal to zero. F(x, y, z, A) = 0 F,(x. y. z, A) = 0 |F,(x, y, z, A) = 0 F.(x, y, z, A) = 0
Example Find the dimensions of the rectangular box with an open top with largest volume if the total surface area is 216 cm².
Transcribed Image Text:Example Find the dimensions of the rectangular box with an open top with largest volume if the total surface area is 216 cm².
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