Show that for both of the following two problems, P = (r, h) is a Lagrange critical
Question:
Show that for both of the following two problems, P = (r, h) is a Lagrange critical point if h = 2r:
• Minimize surface area S for fixed volume V.
• Maximize volume V for fixed surface area S .
Then use the contour plots in Figure 18 to explain why S has a minimum for fixed V but no maximum and, similarly, V has a maximum for fixed S but no minimum.
Transcribed Image Text:
h Increasing S Level curves of S Critical point P = (r, h) Level curve of V Increasing V 1
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (QA)
Answered By
Somshukla Chakraborty
I have a teaching experience of more than 4 years by now in diverse subjects like History,Geography,Political Science,Sociology,Business Enterprise,Economics,Environmental Management etc.I teach students from classes 9-12 and undergraduate students.I boards I handle are IB,IGCSE, state boards,ICSE, CBSE.I am passionate about teaching.Full satisfaction of the students is my main goal.
I have completed my graduation and master's in history from Jadavpur University Kolkata,India in 2012 and I have completed my B.Ed from the same University in 2013. I have taught in a reputed school of Kolkata (subjects-History,Geography,Civics,Political Science) from 2014-2016.I worked as a guest lecturer of history in a college of Kolkata for 2 years teaching students of 1st ,2nd and 3rd year. I taught Ancient and Modern Indian history there.I have taught in another school in Mohali,Punjab teaching students from classes 9-12.Presently I am working as an online tutor with concept tutors,Bangalore,India(Carve Niche Pvt.Ltd.) for the last 1year and also have been appointed as an online history tutor by Course Hero(California,U.S) and Vidyalai.com(Chennai,India).
4.00+
2+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
a. Example 13-1: Batch Reactor with an Exothermic Reaction Wolfram 1. Adiabatic Case: Use Wolfram to see whether you can find a trajectory that is ready to ignite and whose trajectory looks like a...
-
Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...
-
This short exercise demonstrates the similarity and the difference between two ways to acquire plant assets. i (Click the icon to view the cases.) Compare the balances in all the accounts after...
-
In the movie The Drowning Pool, private detective Lew Harper (played by Paul Newman) is trapped by the bad guy in a room containing a swimming pool. The room may be considered rectangular, 5 meters...
-
Given the data and regression analysis for Exercise 15.73, construct and interpret the 90% confidence and prediction intervals associated with 9.0 million new-car registrations x = New-Car...
-
Question: Whitfield, who was black, worked for Ohio Edison. Edison fired him, but then later offered to rehire him. Another employee argued that Edison's original termination of Whitfield had been...
-
Sealing Company manufactures three types of DVD storage units. Each of the three types requires the use of a special machine that has a total operating capacity of 15,000 hours per year. Information...
-
Hoomework help needed - Thanks in advance Betsu, Inc. has previously issued a bond that currently has 7 years left until maturity. The coupon rate of the bond is tied to LIBOR (specifically, its rate...
-
Figure 19 depicts a tetrahedron whose faces lie in the coordinate planes and in the plane with equation The volume of the tetrahedron is given by V = 1/6 abc. Find the minimum value of V among all...
-
Let V be the volume of a can of radius r and height h, and let S be its surface area (including the top and bottom). Find r and h that minimize S subject to the constraint V = 54.
-
Use the Chi-Square Probabilities applet to calculate the p-value for the following chi-square tests: a. X 2 = .81, df = 3 b. X 2 = 25.40, df = 13
-
EXERCISE 3 Arable, Babble and Cradle formed ABC Company with the following initial capital investments: Arable P100,000.00 Babble P200,000.00 Cradle P300,000,00 Compute the share in profits and...
-
Clark Company's current year income statement, comparative balance sheets, and additional information follow. For the year. (1) all sales are credit sales, (2) all credits to Accounts Receivable...
-
Net Income $40,000 Depreciation $8,000 Decrease in Accounts Payable $1,800 Decrease in Inventory $2,500 Increase in Mortgage Payable $10,000 Increase in Common Stock $25,000 Increase in Accounts...
-
At December 31, Palisades and Sherwood submitted the following balances for consolidation. There were no intra- entity payables on that date. Also, Palisades had not yet recorded any goodwill...
-
At the beginning of the year, the company estimated that 54,000 machine-hours would be required for the period's estimated level of production. It also estimated $1,060,000 of fixed manufacturing...
-
Currently, the interest rate on one-year Treasury bonds is 2.2 percent, the rate on two-year Treasury bonds is 3.0 percent, and the rate on three-year Treasury bonds is 3.6 percent. These bonds are...
-
31. What is the income that can be received over 15 years from $500,000 earning 6% annually? 32. What is the semiannual payment required to retire $50,000 in debt over 5 years at 8% compounded...
-
Use the graph shown to determine if the limit exists. If it does, find its value. lim f(x) x4' 6 4 4 2.
-
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), (x) = 3x + 1 x4
-
Graph each function. Use the graph to find the indicated limit, if it exists. lim f(x), f(x) = 2x 1 x-1
-
using Javascript: What is the code for this question? For this task, you need three small images: - one image displays your full name - one image displays your student number - one image displays...
-
This is the project but i'm unable to code and having difficulty understanding overall. The project is about "Automated Water System/Plant", using Arduino but code must be in Java orelse "no mark"....
-
. 6) Add Javadoc comments to your code to fully document what you have created. Below is an example: / * * *This method returns the value of the variable x * / public int getValue () { 7) Download...
Study smarter with the SolutionInn App