An open box of maximum volume is to be made from a square piece of material, s = 30 inches 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.) Height, x Length and Width Volume, V 30 - 2(1) 1[30 – 2(1)]? = 784 1 2 30 - 2(2) 2[30 – 2(2)]2 = 1352 30 – 2(3) |3[30 – 2(3)]² =| 30 - 2(4) 4[30 – 2(4)]² = 4 5 30 – 2(5) 5[30 – 2(5)]² = 6 30 - 2(6) 6[30 – 2(6)]² = Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. V = 0

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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An open box of maximum volume is to be made from a square piece of material, s = 30 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure).
2.
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
1
30 - 2(1)
1[30 – 2(1)]2 = 784
30 - 2(2)
2[30 – 2(2)]2 = 1352
30 - 2(3) 3[30 – 2(3)]2 =
30 - 2(4)
4[30 – 2(4)]2 =
4
30 - 2(5) 5[30 – 2(5)]2 =
30 - 2(6) 6[30 – 2(6)]? =
6
Use the table to guess the maximum volume.
V =
(b) Write the volume V as a function of x.
V =
0 <x< 15
(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 = 30 inches on a side, by cutting equal squares from the corners and turning up the sides (see figure). 2. 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 1 30 - 2(1) 1[30 – 2(1)]2 = 784 30 - 2(2) 2[30 – 2(2)]2 = 1352 30 - 2(3) 3[30 – 2(3)]2 = 30 - 2(4) 4[30 – 2(4)]2 = 4 30 - 2(5) 5[30 – 2(5)]2 = 30 - 2(6) 6[30 – 2(6)]? = 6 Use the table to guess the maximum volume. V = (b) Write the volume V as a function of x. V = 0 <x< 15 (c) Use calculus to find the critical number of the function in part (b) and find the maximum value. V=
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ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage