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An open box of maximum volume is to be made from a square piece of material, s = 36 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 21 (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 36 - 2(1) 1[36 – 2(1)]2 = 1156 36 - 2(2) 2[36 – 2(2)]? = 2048 3 36 – 2(3) 3[36 – 2(3)]² = | 36 – 2(4) 4[36 – 2(4)]² = 4 5 36 - 2(5) 5[36 – 2(5)]? = 6. 36 – 2(6) 6[36 – 2(6)]2 = Use the table to quess the maximum volume. V = (b) Write the volume V as a function of x. V = 0

An open box of maximum volume is to be made from a square piece of material, s = 36 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 21 (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 36 - 2(1) 1[36 – 2(1)]2 = 1156 36 - 2(2) 2[36 – 2(2)]? = 2048 3 36 – 2(3) 3[36 – 2(3)]² = | 36 – 2(4) 4[36 – 2(4)]² = 4 5 36 - 2(5) 5[36 – 2(5)]? = 6. 36 – 2(6) 6[36 – 2(6)]2 = Use the table to quess the maximum volume. V = (b) Write the volume V as a function of x. V = 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 3500 3500 3000 3000 2500 2500 2000 2000 1500 1500 1000 1000 500 500 10 15 10 15 V V 400- 1500- 300 1000 200 500 100 10 15 4. 6
Transcribed Image Text:(d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V 3500 3500 3000 3000 2500 2500 2000 2000 1500 1500 1000 1000 500 500 10 15 10 15 V V 400- 1500- 300 1000 200 500 100 10 15 4. 6
An open box of maximum volume is to be made from a square piece of material, s = 36 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 21 (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 1 36 - 2(1) 1[36 – 2(1)]² = 1156 2 36 - 2(2) 2[36 – 2(2)]² = 2048 3 36 – 2(3) 3[36 – 2(3)]² =| 36 – 2(4) 4[36 – 2(4)]? = 4 36 - 2(5) 5[36 – 2(5)]² = 36 – 2(6) 6[36 – 2(6)]² = 6. Use the table to quess the maximum volume. V = (b) Write the volume V as a function of x. V = 0 <x < 18 (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 = 36 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 21 (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 1 36 - 2(1) 1[36 – 2(1)]² = 1156 2 36 - 2(2) 2[36 – 2(2)]² = 2048 3 36 – 2(3) 3[36 – 2(3)]² =| 36 – 2(4) 4[36 – 2(4)]? = 4 36 - 2(5) 5[36 – 2(5)]² = 36 – 2(6) 6[36 – 2(6)]² = 6. Use the table to quess the maximum volume. V = (b) Write the volume V as a function of x. V = 0 <x < 18 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V =
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