You plan to make a box with a square base and lid, with the largest possible volume, and with surface area 140in^2 a) If the square base of the box is x inches wide, determine a formula for the function V (x) representing the volume of the box (in cubic inches). Your function should contain the variable x and cannot contain any other variables. b) Determine a domain for V(x) which makes sense in the context of the scenario. Briefly explain why you chose the domain you provided c) Determine the largest possible volume of such a box. You must use calculus to verify that the volume you find is the largest possible 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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You plan to make a box with a square base and lid, with the largest possible volume, and with surface area 140in^2

a) If the square base of the box is x inches wide, determine a formula for the function V (x) representing the volume of the box (in cubic inches). Your function should contain the variable x and cannot contain any other variables.

b) Determine a domain for V(x) which makes sense in the context of the scenario. Briefly explain why you chose the domain you provided

c) Determine the largest possible volume of such a box. You must use calculus to verify that the volume you find is the largest possible volume. 

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