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A box with a square base and open top must have a volume of 500 cm. We wish to find the dimensions of the box that minimize the amount of material used. ст First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. 2000 A(x) = 2. Next, find the derivative, A'(x). A' (x) : 2000 Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A'(x) = 0 when x = 10 We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(z) %3D Evaluate A"() at the r-value you gave above.

A box with a square base and open top must have a volume of 500 cm. We wish to find the dimensions of the box that minimize the amount of material used. ст First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. 2000 A(x) = 2. Next, find the derivative, A'(x). A' (x) : 2000 Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A'(x) = 0 when x = 10 We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(z) %3D Evaluate A"() at the r-value you gave above.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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Please help with this answer it's partially wrong, can you please highlight the answers please
A box with a square base and open top must have a volume of 500 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. 2000 A(2) Next, find the derivative, A'(x). A'(x) 2000 Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A'(x) = 0 when x = 10 %3D We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(æ). A"(x) 6. Evaluate A"(x) at the x-value you gave above.
Transcribed Image Text:A box with a square base and open top must have a volume of 500 cm. We wish to find the dimensions of the box that minimize the amount of material used. First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base. Simplify your formula as much as possible. 2000 A(2) Next, find the derivative, A'(x). A'(x) 2000 Now, calculate when the derivative equals zero, that is, when A'(x) = 0. A'(x) = 0 when x = 10 %3D We next have to make sure that this value of x gives a minimum value for the surface area. Let's use the second derivative test. Find A"(æ). A"(x) 6. Evaluate A"(x) at the x-value you gave above.
- E A m QL Valume of box . weith square tox heighe Susface area and the box A = 500 cM3 500 500 AcX) = 2000 ACX) = A'ix) - 2o 00 9x3 = o 1o cM A'cx) hehen x = 1 0 A" (x) = 4 00 0 A"(10) = Arx) iis minim um at x =1ocM the box dlimen Bion of =10X10 = 8 l0o cM? Bage height 5 00 5 cM.
Transcribed Image Text:- E A m QL Valume of box . weith square tox heighe Susface area and the box A = 500 cM3 500 500 AcX) = 2000 ACX) = A'ix) - 2o 00 9x3 = o 1o cM A'cx) hehen x = 1 0 A" (x) = 4 00 0 A"(10) = Arx) iis minim um at x =1ocM the box dlimen Bion of =10X10 = 8 l0o cM? Bage height 5 00 5 cM.
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