. This first example is one you may have seen in precalc. square sheet of cardboard is 3 meters long on each side. You are oing to cut out squares from each corner so that you can fold up the des to make an open box. 3 . Show that the volume of the resulting box is: 4x²-12₂² +9x² - Find the derivative of the volume with respect to x, set that erivative equal to zero and solve for x. What is the domain of interest? And what volume do we get if we use the endpoints? I I L 3 I

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...
Question
1. Optimization Examples
1. This first example is one you may have seen in precalc.
A square sheet of cardboard is 3 meters long on each side. You are
going to cut out squares from each corner so that you can fold up the
sides to make an open box.
3
A. Show that the volume of the resulting box is:
4x²-12₂² +9x²
3_
LLLL
3
B. Find the derivative of the volume with respect to x, set that
derivative equal to zero and solve for x.
C. What is the domain of interest? And what volume do we get if we use the endpoints?
D. Determine the maximum volume -- and convince us that we are done!
I
L---
3
I
I
3
Transcribed Image Text:1. Optimization Examples 1. This first example is one you may have seen in precalc. A square sheet of cardboard is 3 meters long on each side. You are going to cut out squares from each corner so that you can fold up the sides to make an open box. 3 A. Show that the volume of the resulting box is: 4x²-12₂² +9x² 3_ LLLL 3 B. Find the derivative of the volume with respect to x, set that derivative equal to zero and solve for x. C. What is the domain of interest? And what volume do we get if we use the endpoints? D. Determine the maximum volume -- and convince us that we are done! I L--- 3 I I 3
Expert Solution
Step 1

To find out the volume of the remaining box.

steps

Step by step

Solved in 2 steps

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
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: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning