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An open box of maximum volume is to be made from a square piece of material, s = 24 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 and Width 24 - 2(1) 24 - 2(2) 24-2(3) 3[24 - 2(3)]² = [ 242(4) 4[24-2(4)]²=| 24-2(5) 5[24-2(5)]² = [ 242(6) 6[242(6)]²= Height, x 1 V = 2 3 4 5 s-2x 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. Volume, V 1[242(1)]² 484 2[24 - 2(2)]² = 800 0 < x < 12 (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 = 24 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 and Width 24 - 2(1) 24 - 2(2) 24-2(3) 3[24 - 2(3)]² = [ 242(4) 4[24-2(4)]²=| 24-2(5) 5[24-2(5)]² = [ 242(6) 6[242(6)]²= Height, x 1 V = 2 3 4 5 s-2x 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. Volume, V 1[242(1)]² 484 2[24 - 2(2)]² = 800 0 < x < 12 (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
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 maximum volume is to be made from a square piece of material, s = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). XT -x7-8 (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width 24 - 2(1) 24 - 2(2) 24 2(3) V Height, X 1 2 3 4 5 s-2x 6 Volume, V 1[242(1)]2 484 2[24-2(2)]² = 800 3[24 - 2(3)]²= | 4[24 - 2(4)]²= 242(4) 242(5) 5[24 - 2(5)]² = 242(6) 6[242(6)]²= Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0 < x < 12 (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 maximum volume is to be made from a square piece of material, s = 24 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). XT -x7-8 (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width 24 - 2(1) 24 - 2(2) 24 2(3) V Height, X 1 2 3 4 5 s-2x 6 Volume, V 1[242(1)]2 484 2[24-2(2)]² = 800 3[24 - 2(3)]²= | 4[24 - 2(4)]²= 242(4) 242(5) 5[24 - 2(5)]² = 242(6) 6[242(6)]²= Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0 < x < 12 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =
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Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V 1000 800 600 400 200 V 1000 800 600 400 200 2 4 6 8 2 4 6 8 10 10 12 12 X X 120 100 80 60 40 20 1 500 2 N 400 300 n 200 100 3 4 4 6 8 00 5 10 01 12 X X
Transcribed Image Text:Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V 1000 800 600 400 200 V 1000 800 600 400 200 2 4 6 8 2 4 6 8 10 10 12 12 X X 120 100 80 60 40 20 1 500 2 N 400 300 n 200 100 3 4 4 6 8 00 5 10 01 12 X X
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