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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). S-2x (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 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)]? - | 4 12-2(4) 4[12 - 2(4)]? - 5 12-2(5) 5[12- 2(5)]? - | 6. 12- 2(6) 6[12 - 2(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.) Height, x Length and Width 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)]? - | 4 12-2(4) 4[12 - 2(4)]? - 5 12-2(5) 5[12- 2(5)]? - | 6. 12- 2(6) 6[12 - 2(6)]? =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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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). S- 2x (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 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)]? - | 4 12 - 2(4) 4[12 – 2(4)]² = 12 - 2(5) 5[12 – 2(5)]? | 6. 12 - 2(6) 6[12 – 2(6)]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.) Height, x Length and Width 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)]? - | 4 12 - 2(4) 4[12 – 2(4)]² = 12 - 2(5) 5[12 – 2(5)]? | 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 graphíng 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 20 3 X 3.0 4. 5. 6. 0.5 1.0 1.5 2.0 2.5 60 120
Transcribed Image Text: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 graphíng 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 20 3 X 3.0 4. 5. 6. 0.5 1.0 1.5 2.0 2.5 60 120
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