Homework Help is Here – Start Your Trial Now!
Math
Calculus
1. Solve the following problems with the second partial derivative test and with Lagrange's method. a). Find the volume of a rectangular box with maximum volume if the sum its 12 edges is a constant c. b). The base of an aquarium of volume V is made of stone, and its sides are made of glass. If the stone costs 5 times the glass (per unit area), find the size of the aquarium that minimize the cost of materials. c). A cardboard box without lid will be built to contain 32 000 cm³. Find the dimensions of the box that minimize the amount of paperboard used.

1. Solve the following problems with the second partial derivative test and with Lagrange's method. a). Find the volume of a rectangular box with maximum volume if the sum its 12 edges is a constant c. b). The base of an aquarium of volume V is made of stone, and its sides are made of glass. If the stone costs 5 times the glass (per unit area), find the size of the aquarium that minimize the cost of materials. c). A cardboard box without lid will be built to contain 32 000 cm³. Find the dimensions of the box that minimize the amount of paperboard used.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
See similar textbooks
icon
Related questions
Question

show full and complete procedure HANDWRITTEN only

1. Solve the following problems with the second partial derivative test and with Lagrange's method. a) . Find the volume of a rectangular box with maximum volume if the sum of its 12 edges is a constant c. b). The base of an aquarium of volume V is made of stone, and its sides are made of glass. If the stone costs 5 times the glass (per unit area), find the size of the aquarium that minimize the cost of materials. c). A cardboard box without lid will be built to contain 32 000 cm³. Find the dimensions of the box that minimize the amount of paperboard used.
Transcribed Image Text:1. Solve the following problems with the second partial derivative test and with Lagrange's method. a) . Find the volume of a rectangular box with maximum volume if the sum of its 12 edges is a constant c. b). The base of an aquarium of volume V is made of stone, and its sides are made of glass. If the stone costs 5 times the glass (per unit area), find the size of the aquarium that minimize the cost of materials. c). A cardboard box without lid will be built to contain 32 000 cm³. Find the dimensions of the box that minimize the amount of paperboard used.
Expert Solution
steps

Step by step

Solved in 9 steps with 9 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS