Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.2 - Polynomial Functions and Their Graphs - 3.2 Exercises - Page 268: 90

Answer

(a) see prove. (b) $0\lt x\lt 18$ (c) $1728$

Work Step by Step

(a) The height of the box is $\frac{144-8x}{4}=36-2x$ and the volume is $V=x^2(36-2x)=2x^2(18-x)$ (b) Let $18-x\gt 0$ we have the domain as $0\lt x\lt 18$ (c) The graph shows that the maximum happens at $x=12in, V=1728in^3$
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