A box with a square base and open top must have a volume of 108000 cm3cm3. 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 xx, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of xx.] Simplify your formula as much as possible. A(x)= Next, find the derivative, A'(x)A′(x). A'(x)=A′(x)= Now, calculate when the derivative equals zero, that is, when A'(x)=0A′(x)=0. [Hint: multiply both sides by x2x2.] A'(x)=0A′(x)=0 when x=
A box with a square base and open top must have a volume of 108000 cm3cm3. 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 xx, the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of xx.] Simplify your formula as much as possible. A(x)= Next, find the derivative, A'(x)A′(x). A'(x)=A′(x)= Now, calculate when the derivative equals zero, that is, when A'(x)=0A′(x)=0. [Hint: multiply both sides by x2x2.] A'(x)=0A′(x)=0 when x=
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...
Related questions
Question
A box with a square base and open top must have a volume of 108000 cm3cm3. 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 xx, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in terms of xx.]
Simplify your formula as much as possible.
A(x)=
Next, find the derivative, A'(x)A′(x).
A'(x)=A′(x)=
Now, calculate when the derivative equals zero, that is, when A'(x)=0A′(x)=0. [Hint: multiply both sides by x2x2.]
A'(x)=0A′(x)=0 when x=
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning