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An open box of maximum volume is to be made from a square piece of material, s = 12 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 2: S- 2x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width Height, x Volume, V 12 - 2(1) 1[12 – 2(1)]? = 100 1 2 12 - 2(2) 2[12 – 2(2)]² = 128 12 - 2(3) 3[12 - 2(3)]² = [ 12 - 2(4) 4[12 – 2(4)]? = | 4. 12 - 2(5) 5[12 - 2(5)]² =| 12 - 2(6) 6[12 – 2(6)]² = [ Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. 0

An open box of maximum volume is to be made from a square piece of material, s = 12 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 2: S- 2x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width Height, x Volume, V 12 - 2(1) 1[12 – 2(1)]? = 100 1 2 12 - 2(2) 2[12 – 2(2)]² = 128 12 - 2(3) 3[12 - 2(3)]² = [ 12 - 2(4) 4[12 – 2(4)]? = | 4. 12 - 2(5) 5[12 - 2(5)]² =| 12 - 2(6) 6[12 – 2(6)]² = [ 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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(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V 60 120 50 100 40 80 30 60 20 40 10 20 X 6 1 2 3 4 5 6 1 3 5 nn V V 15 120 100 10 80 60 5 40 20 X X 3.0 0.5 1.0 1.5 2.0 2.5 1 2 3 4
Transcribed Image Text:(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V 60 120 50 100 40 80 30 60 20 40 10 20 X 6 1 2 3 4 5 6 1 3 5 nn V V 15 120 100 10 80 60 5 40 20 X X 3.0 0.5 1.0 1.5 2.0 2.5 1 2 3 4
An open box of maximum volume is to be made from a square piece of material, s = 12 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). XT S- 2x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width Height, x Volume, V 12 – 2(1) 1[12 – 2(1)]2 = 100 2 12 - 2(2) 2[12 – 2(2)]2 = 128 3 12 - 2(3) 3[12 – 2(3)]? = 12 - 2(4) 4[12 - 2(4)]? = 4 12 - 2(5) 5[12 – 2(5)]? = 6 12 - 2(6) 6[12 – 2(6)]? = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. V = 0 < x< 6 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V = (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. s – 2x
Transcribed Image Text:An open box of maximum volume is to be made from a square piece of material, s = 12 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). XT S- 2x (a) Analytically complete six rows of a table such as the one below. (The first two rows are shown.) Length and Width Height, x Volume, V 12 – 2(1) 1[12 – 2(1)]2 = 100 2 12 - 2(2) 2[12 – 2(2)]2 = 128 3 12 - 2(3) 3[12 – 2(3)]? = 12 - 2(4) 4[12 - 2(4)]? = 4 12 - 2(5) 5[12 – 2(5)]? = 6 12 - 2(6) 6[12 – 2(6)]? = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. V = 0 < x< 6 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V = (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. s – 2x
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