An open box of maximum volume is to be made from a square piece of material, s = 18 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). S- 2x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, x Length and Width Volume, V 18 - 2(1) 1[18 - 2(1)]2 = 256 18 - 2(2) 2[18 - 2(2)]2 = 392 2 18 - 2(3) 3[18 - 2(3)]2 =| 3 18 - 2(4) 4[18 - 2(4)]2 = 4 18 - 2(5) 5[18 - 2(5)]2 = | 18 - 2(6) 6[18 - 2(6)]2 = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0 < x< 9 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =
An open box of maximum volume is to be made from a square piece of material, s = 18 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). S- 2x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Height, x Length and Width Volume, V 18 - 2(1) 1[18 - 2(1)]2 = 256 18 - 2(2) 2[18 - 2(2)]2 = 392 2 18 - 2(3) 3[18 - 2(3)]2 =| 3 18 - 2(4) 4[18 - 2(4)]2 = 4 18 - 2(5) 5[18 - 2(5)]2 = | 18 - 2(6) 6[18 - 2(6)]2 = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0 < x< 9 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.4: Complex And Rational Zeros Of Polynomials
Problem 39E
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