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W W W The length of the box, as a function of x, is l = The width of the box, as a function of x, is w The volume of the box, as a function of x, is V = V(x) = which, after distributing, simplifies to V : V(x) = To determine the value of x that corresponds to a maximum volume, we need to find V'. V' Solving V' = 0 → x = inches and the maximum volume is V cubic inches

W W W The length of the box, as a function of x, is l = The width of the box, as a function of x, is w The volume of the box, as a function of x, is V = V(x) = which, after distributing, simplifies to V : V(x) = To determine the value of x that corresponds to a maximum volume, we need to find V'. V' Solving V' = 0 → x = inches and the maximum volume is V cubic inches

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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W W W The length of the box, as a function of x, is l = The width of the box, as a function of x, is w The volume of the box, as a function of x, is V = V(x) = which, after distributing, simplifies to V : V(x) = To determine the value of x that corresponds to a maximum volume, we need to find V'. V' Solving V' = 0 = x = inches and the maximum volume is V cubic inches
Transcribed Image Text:W W W The length of the box, as a function of x, is l = The width of the box, as a function of x, is w The volume of the box, as a function of x, is V = V(x) = which, after distributing, simplifies to V : V(x) = To determine the value of x that corresponds to a maximum volume, we need to find V'. V' Solving V' = 0 = x = inches and the maximum volume is V cubic inches
Given a W = 8 inch by L = 15 inch piece of paper, we will cut out squares(size x by x) from each corner and fold to create an (open top) box. Our goal is to find the size of the cut out square ( x), that maximizes the volume of the box. W W W The length of the box, as a function of x, is l The width of the box, as a function of x, is w = The volume of the box, as a function of x, is V = V(x) = which, after distributing, simplifies to V = V(x) = To determine the value of x that corresponds to a maximum volume, we need to find V'. V'
Transcribed Image Text:Given a W = 8 inch by L = 15 inch piece of paper, we will cut out squares(size x by x) from each corner and fold to create an (open top) box. Our goal is to find the size of the cut out square ( x), that maximizes the volume of the box. W W W The length of the box, as a function of x, is l The width of the box, as a function of x, is w = The volume of the box, as a function of x, is V = V(x) = which, after distributing, simplifies to V = V(x) = To determine the value of x that corresponds to a maximum volume, we need to find V'. V'
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