Stitz-Zeager_College_Algebra_e-book

# Theorem 33 the role of multiplicity suppose f is a

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Unformatted text preview: t congruent squares from each corner of the cardboard and then folding the resulting tabs. Let x denote the length of the side of the square which is removed from each corner. x x x x 12 in height x x x depth width x 10 in 1. Find the volume V of the box as a function of x. Include an appropriate applied domain. 2. Use a graphing calculator to graph y = V (x) on the domain you found in part 1 and approximate the dimensions of the box with maximum volume to two decimal places. What is the maximum volume? Solution. 1. From Geometry, we know Volume = width × height × depth. The key is to now ﬁnd each of these quantities in terms of x. From the ﬁgure, we see the height of the box is x itself. The cardboard piece is initially 10 inches wide. Removing squares with a side length of x inches from each corner leaves 10 − 2x inches for the width.5 As for the depth, the cardboard is initially 12 inches long, so after cutting out x inches from each side, we would have 12 − 2x inches remaining. As a function6 of x, the volume is V (x) = x(10 − 2x)(1...
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## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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