A box with a square base and open top must have a volume of 275684 cm³. 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 æ, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of æ.] Simplify your formula as much as possible. A(x) = | Next, find the derivative, A'(x). A'(x) = Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by æ?.] A' (x) = 0 when a = We next have to make sure that this value of a gives a minimum value for the surface area. Let's use the second derivative test. Find A"(x). A"(x) = Evaluate A"(x) at the x-value you gave above.

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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A box with a square base and open top must have a volume of 275684 cm³. 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.
[Hint: use the volume formula to express the height of the box in terms of x.]
Simplify your formula as much as possible.
A(x) =
Next, find the derivative, A’(x).
= (x),V
Now, calculate when the derivative equals zero, that is, when A'(x)
sides by x?.]
A' (x) =
0. [Hint: multiply both
%3D
O when x =
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"(x) =
Evaluate A"(x) at the x-value you gave above.
11:14 AM
22
12/16/2021
...
治
Transcribed Image Text:M MyOpenMath A myopenmath.com/assess2/?cid=123243&aid=8821253#/skip/1 A : Apps M Gmail YouTube Мaps u Adobe Photoshop... N Nucly 7 Are You Solving the... My dashboard 7 Deciding How to D... 2.3 Issue Trees - Spr.. E Reading list >> Textbook G O Videos L'+| A box with a square base and open top must have a volume of 275684 cm³. 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. [Hint: use the volume formula to express the height of the box in terms of x.] Simplify your formula as much as possible. A(x) = Next, find the derivative, A’(x). = (x),V Now, calculate when the derivative equals zero, that is, when A'(x) sides by x?.] A' (x) = 0. [Hint: multiply both %3D O when x = 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"(x) = Evaluate A"(x) at the x-value you gave above. 11:14 AM 22 12/16/2021 ... 治
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