A box with no top is to be built by taking a sheet of cardboard measuring 18-inches by 22-inches, cutting z-inch squares out of each corner, and folding up the sides. a) What are the length and width of the base of the box, after it is folded? It may help to draw a picture showing the cardboard before it is folded, and then draw another picture showing the resulting box. Length: b) What is the volume of the resulting box? Write your answer as a function of z. Volume: c) What is the domain of this function? In other words, what values of a make sense? (Think about the original problem.) Domain: Width: d) Find all of the critical points of this function (not just on the given domain). Critical points at: ==
A box with no top is to be built by taking a sheet of cardboard measuring 18-inches by 22-inches, cutting z-inch squares out of each corner, and folding up the sides. a) What are the length and width of the base of the box, after it is folded? It may help to draw a picture showing the cardboard before it is folded, and then draw another picture showing the resulting box. Length: b) What is the volume of the resulting box? Write your answer as a function of z. Volume: c) What is the domain of this function? In other words, what values of a make sense? (Think about the original problem.) Domain: Width: d) Find all of the critical points of this function (not just on the given domain). Critical points at: ==
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:A box with no top is to be built by taking a sheet of cardboard measuring 18-inches by 22-inches, cutting z-inch squares out of
each corner, and folding up the sides.
a) What are the length and width of the base of the box, after it is folded? It may help to draw a picture showing the cardboard
before it is folded, and then draw another picture showing the resulting box.
Length:
b) What is the volume of the resulting box? Write your answer as a function of z.
Volume:
Width:
c) What is the domain of this function? In other words, what values of a make sense? (Think about the original problem.)
Domain:
d) Find all of the critical points of this function (not just on the given domain).
Critical points at: a =
e) Find the absolute maximum of this function within its domain.
Absolute maximum:
cubic inches
f) What size squares should be cut out of the corners to maximize the volume of the resulting box?
Size of squares: -inches wide squares
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