Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 1 - Section 1.1 - Four Ways to Represent a Function - 1.1 Exercises - Page 22: 63


$V(x)=4x^{3}-64x^{2}+240x, 0\lt x\lt6$

Work Step by Step

Length of box = $20-2x$ Width of box = $12-2x$ Height of box = $x$ Volume = Length$\times$Width$\times$Height =$x(20-2x)(12-2x)$ =$4x(10-x)(6-x)$ =$4x(x^{2}-16x+60)$ =$4x^{3}-64x^{2}+240x$ $\because$ All lengths are positive, Length = $20-2x\gt0, x\lt10$ Width = $12-2x\gt0, x\lt6$ Height = $x\gt0$ $\therefore 0\lt x\lt6$
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