2. An open box will be made by cutting a square from each corner of a 6-ft by 6-ft piece of cardboard and then folding up the sides. Let x be the length of the side of the square. a).. Set up the volume of the box as a function of r: V(r), find the domain. b). Find V'(x), and find the critical numbers. c). Find the r value that produces a box of maximum volume. d). What is the maximum volume.

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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2. An open box will be made by cutting a square from each corner of a 6-ft by 6-ft piece of
cardboard and then folding up the sides. Let x be the length of the side of the square. a)..
Set up the volume of the box as a function of x: V (x), find the domain. b). Find V'(x), and
find the critical numbers. c). Find the r value that produces a box of maximum volume. d).
What is the maximum volume.
Transcribed Image Text:2. An open box will be made by cutting a square from each corner of a 6-ft by 6-ft piece of cardboard and then folding up the sides. Let x be the length of the side of the square. a).. Set up the volume of the box as a function of x: V (x), find the domain. b). Find V'(x), and find the critical numbers. c). Find the r value that produces a box of maximum volume. d). What is the maximum volume.
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