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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 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 Height, x Volume, V Width 1 12 - 2(1) 1[12 - 2(1)]2 = 100 2. 12 - 2(2) 2[12 - 2(2)]? = 128 31 12 2(3) 3[12 - 2(3)]2 = 12 - 2(4) 4[12 - 2(4))? = 4 5. 12 - 2(5) 5[12 - 2(5)]? = 12 - 2(6) 6[12 - 2(6)]? = Use the table to guess the maximum volume. V = (b) Write the volume Vas a function of x. V = OSx< 6 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V= from the oanh

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 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 Height, x Volume, V Width 1 12 - 2(1) 1[12 - 2(1)]2 = 100 2. 12 - 2(2) 2[12 - 2(2)]? = 128 31 12 2(3) 3[12 - 2(3)]2 = 12 - 2(4) 4[12 - 2(4))? = 4 5. 12 - 2(5) 5[12 - 2(5)]? = 12 - 2(6) 6[12 - 2(6)]? = Use the table to guess the maximum volume. V = (b) Write the volume Vas a function of x. V = OSx< 6 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V= from the oanh

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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Imu the cnticalnu mber oi Lhe TuncLron in part (D) ana inu the maximurm value. (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 120 15 100 80 10 60 40 51 20 X 1 2 3 4 5 0.5 1.0 1.5 2.0 2.5 3.0 V V 60 120 50 100 40 80 30 60 20 40 10 20 1 2 4 5 1 2 3 4 5 6
Transcribed Image Text:Imu the cnticalnu mber oi Lhe TuncLron in part (D) ana inu the maximurm value. (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 120 15 100 80 10 60 40 51 20 X 1 2 3 4 5 0.5 1.0 1.5 2.0 2.5 3.0 V V 60 120 50 100 40 80 30 60 20 40 10 20 1 2 4 5 1 2 3 4 5 6
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). 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 12 2(2) 2[12 – 2(2)]² = 128 3 12 2(3) 3[12 – 2(3)]² = 4 12 - 2(4) 4[12 - 2(4)]? %3D | 5 12 – 2(5) 5[12 – 2(5)]² = | %3D 6. 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. 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. V V 120 15 100 80 10 60 S-2x 2.
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). 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 12 2(2) 2[12 – 2(2)]² = 128 3 12 2(3) 3[12 – 2(3)]² = 4 12 - 2(4) 4[12 - 2(4)]? %3D | 5 12 – 2(5) 5[12 – 2(5)]² = | %3D 6. 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. 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. V V 120 15 100 80 10 60 S-2x 2.
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