An open-top box is to be constructed from a 4 in by 16 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let a denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, V, of the box as a function of x. V(x) = (b) For what values of a does the formula from part (a) make sense in the context of the problem? help (inequalities) (c) On a separate piece of paper, sketch a graph of the volume function. (d) What, approximately, is the maximum volume of the box? (include units: help (units))
An open-top box is to be constructed from a 4 in by 16 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let a denote the length of the side of each cut-out square. Assume negligible thickness. (a) Find a formula for the volume, V, of the box as a function of x. V(x) = (b) For what values of a does the formula from part (a) make sense in the context of the problem? help (inequalities) (c) On a separate piece of paper, sketch a graph of the volume function. (d) What, approximately, is the maximum volume of the box? (include units: help (units))
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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Transcribed Image Text:An open-top box is to be constructed from a 4 in by 16 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let e denote the length of the side of each cut-out
square. Assume negligible thickness.
(a) Find a formula for the volume, V, of the box as a function of x. V(x):
=
(b) For what values of a does the formula from part (a) make sense in the context of the problem?
help (inequalities)
(c) On a separate piece of paper, sketch a graph of the volume function.
(d) What, approximately, is the maximum volume of the box?
(include units: help (units))
Transcribed Image Text:Find all of the zeros of the function f(x) = (x² + 2x − 12) (x³ + x² — 12x). If there is more than one answer, enter your answers as a comma separated list. If there are no zeros, enter NONE. Enter exact answers, not
decimal approximations.
x = -help (numbers)
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