A box with a square base and open top must have a volume of 442368 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. [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) = %3D Next, find the derivative, A'(x). A'(파) %= %3D Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x.] %3D A'(x) = 0 when a = 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) %3D Evaluate A"(x) at the x-value you gave bove. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x). (Your boss is happy now.)
A box with a square base and open top must have a volume of 442368 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. [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) = %3D Next, find the derivative, A'(x). A'(파) %= %3D Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x.] %3D A'(x) = 0 when a = 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) %3D Evaluate A"(x) at the x-value you gave bove. NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value, so the zero of A'(x) must indicate a local minimum for A(x). (Your boss is happy now.)
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
Chapter2: Graphical And Tabular Analysis
Section2.4: Solving Nonlinear Equations
Problem 2TU
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![* 00
T
A box with a square base and open top must have a volume of 442368 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.
[Hint: use the volume formula to express the height of the box in terms of x.]
Simplify your formula as much as possible.
%3D
Next, find the derivative, A'(x).
(2), V
Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x.]
%3D
A'(x) = 0 when x =
%3D
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).
%3D
Evaluate A"(x) at the x-value you gave bove.
NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value,
so the zero of A'(x) must indicate a local minimum for A(x). (Your boss is happy now.)
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Transcribed Image Text:* 00
T
A box with a square base and open top must have a volume of 442368 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.
[Hint: use the volume formula to express the height of the box in terms of x.]
Simplify your formula as much as possible.
%3D
Next, find the derivative, A'(x).
(2), V
Now, calculate when the derivative equals zero, that is, when A'(x) = 0. [Hint: multiply both sides by x.]
%3D
A'(x) = 0 when x =
%3D
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).
%3D
Evaluate A"(x) at the x-value you gave bove.
NOTE: Since your last answer is positive, this means that the graph of A(x) is concave up around that value,
so the zero of A'(x) must indicate a local minimum for A(x). (Your boss is happy now.)
Submit Question
Jump to Answer
MacBook Pro
#3
3.
24
2
4.
9-
7.
|
G.
H.
K.
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