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An open box of max material, s = 24 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). Volume is to be made from a square piece of S-2r- (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 1 24 - 2(1) 1[24 - 2(1)]? = 484 2 24 - 2(2) 2[24 - 2(2)]? - 800 24 - 2(3) 3(24 - 2(3)]? - 3 24 - 2(4) 4[24 - 2(4)]? 4 24 - 2(5) 5[24 - 2(5))? 5 24 - 2(6) 6[24 - 2(6)? = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0

An open box of max material, s = 24 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). Volume is to be made from a square piece of S-2r- (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 1 24 - 2(1) 1[24 - 2(1)]? = 484 2 24 - 2(2) 2[24 - 2(2)]? - 800 24 - 2(3) 3(24 - 2(3)]? - 3 24 - 2(4) 4[24 - 2(4)]? 4 24 - 2(5) 5[24 - 2(5))? 5 24 - 2(6) 6[24 - 2(6)? = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0

Algebra & Trigonometry with Analytic Geometry
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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An open box of max material, s = 24 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). Volume is to be made from a square piece of S-2r- (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 1 24 - 2(1) 1[24 - 2(1)]? = 484 2 24 - 2(2) 2[24 - 2(2)]? - 800 24 - 2(3) 3(24 - 2(3)]? - 3 24 - 2(4) 4[24 - 2(4)]? 4 24 - 2(5) 5[24 - 2(5))? 5 24 - 2(6) 6[24 - 2(6)? = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0<x < 12 V= (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =
Transcribed Image Text:An open box of max material, s = 24 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). Volume is to be made from a square piece of S-2r- (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 1 24 - 2(1) 1[24 - 2(1)]? = 484 2 24 - 2(2) 2[24 - 2(2)]? - 800 24 - 2(3) 3(24 - 2(3)]? - 3 24 - 2(4) 4[24 - 2(4)]? 4 24 - 2(5) 5[24 - 2(5))? 5 24 - 2(6) 6[24 - 2(6)? = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0<x < 12 V= (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =
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