An open box of maximum volume is tomade from a square piecematerial, s= 18 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure).(a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.)Length andWidthHeight,Volume, V18 - 2(1)1[18 - 2(1)12 - 2561218 - 2(2)2[18 - 2(2)]? - 39218 - 2(3) 3[18 - 2(3)]2 -318 - 2(4) 4[18 - 2(4)]2 -|418 - 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.V-(c) Use calculus to find the critical number of the function in part (b) and find the maximum value. (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph.VV504004030030200201001024.6.8V400200300150200100100506

Given:- An open box of maximum volume is to e made from a square piece of material, s 18 centimeters…

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). (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[16 - 2(1)12 - 256 18 - 2(2) 2[18 - 2(2)12 - 292 2 18 - 2(3) a[18 - 2(3))2 - 3 18 - 2(4) 4[18 - 2(4)]2 - 4 18 - 2(5) 5(18 - 2(5)]2 = [ 5 18 - 2(6) 6[18 - 2(6))2 - [ 6 Use the table to guess the maximum volume. (b) Write the volume V as a function of x. O

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). (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[16 - 2(1)12 - 256 18 - 2(2) 2[18 - 2(2)12 - 292 2 18 - 2(3) a[18 - 2(3))2 - 3 18 - 2(4) 4[18 - 2(4)]2 - 4 18 - 2(5) 5(18 - 2(5)]2 = [ 5 18 - 2(6) 6[18 - 2(6))2 - [ 6 Use the table to guess the maximum volume. (b) Write the volume V as a function of x. O

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 67E

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