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an open box of maximum volume is to be made from a square piece of material, s = 30 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 21 :-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 30 - 2(1) 1[30 - 2(1)]? = 784 2 30 - 2(2) 2[30 - 2(2)12 = 1352 30 - 2(3) 3(30 - 2(3)12 = [ 3 30 - 2(4) 4[30 - 2(4)]? = 4 30 - 2(5) S(30 - 2(5)12 =| 5. 30 - 2(6) 6[30 - 2(6))? = 6 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 = 30 centimeters on a side, by cutting equal squares from the corners and turning up the sides (see figure). 21 :-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 30 - 2(1) 1[30 - 2(1)]? = 784 2 30 - 2(2) 2[30 - 2(2)12 = 1352 30 - 2(3) 3(30 - 2(3)12 = [ 3 30 - 2(4) 4[30 - 2(4)]? = 4 30 - 2(5) S(30 - 2(5)12 =| 5. 30 - 2(6) 6[30 - 2(6))? = 6 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
Section4.3: Zeros Of Polynomials
Problem 67E
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(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 1000 2000 800 1500 600 1000 400 200 500 2 4 6. 8. 10 12 14 2 4 6. 8 10 12 14 250 V 2000| 200 1500 150 1000 100 50 500 3 4 6. 7. 2 4 6 8. 10 12 14 Submit Answer
Transcribed Image Text:(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 1000 2000 800 1500 600 1000 400 200 500 2 4 6. 8. 10 12 14 2 4 6. 8 10 12 14 250 V 2000| 200 1500 150 1000 100 50 500 3 4 6. 7. 2 4 6 8. 10 12 14 Submit Answer
An open box of maximum volume is to be made from a square piece of material, s = 30 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 30 2(1) 1[30 - 2(1)12 = 784 2 30 - 2(2) 2[30 - 2(2)]2 = 1352 3. 30 - 2(3) 3(30 - 2(3))2 = 30 2(4) 4[30 - 2(4))? = 4. 30 - 2(5) s(30 - 2(5)1? = 30 - 2(6) 6[30 - 2(6)1 = 6. Use the table to quess the maximum volume. V = (b) Write the volume V as a function of x. V = O<x< 15 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 1000- 2000 800 1500 600 1000 400
Transcribed Image Text:An open box of maximum volume is to be made from a square piece of material, s = 30 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 30 2(1) 1[30 - 2(1)12 = 784 2 30 - 2(2) 2[30 - 2(2)]2 = 1352 3. 30 - 2(3) 3(30 - 2(3))2 = 30 2(4) 4[30 - 2(4))? = 4. 30 - 2(5) s(30 - 2(5)1? = 30 - 2(6) 6[30 - 2(6)1 = 6. Use the table to quess the maximum volume. V = (b) Write the volume V as a function of x. V = O<x< 15 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. (d) Use a graphing utility to graph the function in part (b) and verify the maximum volume from the graph. V V 1000- 2000 800 1500 600 1000 400
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