Show that the Lagrange equations for (x, y) = 2x + y subject to the constraint g(x,
Question:
Show that the Lagrange equations for ƒ(x, y) = 2x + y subject to the constraint g(x, y) = x2 − y2 = 1 have a solution but that f has no min or max on the constraint curve. Does this contradict Theorem 1?
Transcribed Image Text:
THEOREM 1 Lagrange Multipliers Assume that f(x, y) and g(x, y) are differen- tiable functions. If f(x, y) has a local minimum or a local maximum on the constraint curve g(x, y) = 0 at P = (a, b), and if Vgp #0, then there is a scalar such that Vfp = Vgp
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 100% (1 review)
or and hence Using the methods of Lagrange we can write Vf Vg and see 2 1 2x 2y 2 21x Ev...View the full answer
Answered By
Keziah Thiga
I am a self motivated financial professional knowledgeable in; preparation of financial reports, reconciling and managing accounts, maintaining cash flows, budgets, among other financial reports. I possess strong analytical skills with high attention to detail and accuracy. I am able to act quickly and effectively when dealing with challenging situations. I have the ability to form positive relationships with colleagues and I believe that team work is great key to performance. I always deliver quality, detailed, original (0% plagirism), well-researched and critically analyzed papers.
4.90+
1504+ Reviews
2898+ Question Solved
Related Book For
Question Posted:
Students also viewed these Mathematics questions
-
Find the extreme values of (x, y) = x 2 + 2y 2 subject to the constraint g(x, y) = 4x 6y = 25. (a) Show that the Lagrange equations yield 2x = 42, 4y = -62. (b) Show that if x = 0 or y = 0, then the...
-
Show that the Lagrange equations for (x, y) = x + y subject to the constraint g(x, y) = x + 2y = 0 have no solution. What can you conclude about the minimum and maximum values of f subject to g = 0?...
-
Consider the problem of minimizing (x, y) = x subject to g(x, y) = (x 1) 3 y 2 = 0. (a) Show, without using calculus, that the minimum occurs at P = (1, 0). (b) Show that the Lagrange condition P =...
-
Data on the length, in seconds, of a sample of 50 songs by The Beatles are presented in the accompanying data table. Complete parts (a) through (d) below. Click the icon to view the table of song...
-
The level of toluene (a flammable hydrocarbon) in a storage tank may fluctuate between 10 and 400 cm from the top of the tank. Since it is impossible to see inside the tank, and open-end manometer...
-
Outdoor Amenities is a manufacturer of backyard and deck furniture. Its products are in high demand, and it carries no inventory. Following is a list of selected account balances from its trial...
-
The cantilevered beam is subjected to a couple moment \(\mathbf{M}_{0}\) applied at its end. Determine the slope of the beam at \(B\). \(E I\) is constant. Use the method of virtual work. A -L B Mo
-
Enter the following cash payments transactions in a general journal: Sept. 5 Issued Check No. 318 to Clinton Corp. for merchandise purchased August 28, $6,000, terms 2/10, n/30. Payment is made...
-
Presented below is information related to plant assets and intangible assets at year-end on December 31, 2025 for Wildhorse Co.: Buildings Goodwill Patents $1,132,800 355,200 460,800 Land 374,400...
-
Let L be the minimum length of a ladder that can reach over a fence of height h to a wall located a distance b behind the wall. (a) Use Lagrange multipliers to show that L = (h/3 + b2/3 3/2 (Figure...
-
With the same set-up as in the previous problem, find the plane that minimizes V if the plane is constrained to pass through a point P = (, , ) with , , > 0.
-
Find the sums of the given infinite geometric series. 1280 320 + 80 . . .
-
Chamber \(\mathrm{X}\) contains monatomic ideal gas \(\mathrm{X}\). The gas particles have a root-mean-square speed of \(42 \mathrm{~m} / \mathrm{s}\). Chamber Y, identical to chamber X, contains a...
-
A sealed \(1.50-\mathrm{L}\) chamber filled with helium gas initially at \(20^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) is heated until the gas temperature is \(232^{\circ} \mathrm{C}\). (a)...
-
The atoms of an element can come in different forms, depending on the number of neutrons in the nucleus. These different forms are called isotopes of the element. The two most common isotopes of...
-
Consider a helium atom that is part of Earth's atmosphere and is initially at the planet's surface, where the temperature is \(20^{\circ} \mathrm{C}\). To what maximum altitude can this atom rise if...
-
The temperature of the Sun's corona (the outermost gas layer) is \(1.0 \times 10^{6} \mathrm{~K}\), and this layer is just above the photosphere layer, which has a radius of \(6.96 \times 10^{8}...
-
Access the glossary (Master Glossary) to answer the following. (a) What is the definition of present value? (b) Briefly describe the term discount rate adjustment technique. (c) Identify the other...
-
Keating & Partners is a law firm specializing in labour relations and employee-related work. It employs 25 professionals (5 partners and 20 managers) who work directly with its clients. The average...
-
Use a table to find the indicated limit. lim x0 x + 4 ,2
-
Use a table to find the indicated limit. x - 4x lim x4 x 4
-
Use a table to find the indicated limit. lim x3 x 3x
-
Suppose the domestic price level increases by 15%, the exchange rate of domestic currency per foreign currency increases by 27%, and the foreign price level increases by 3%. What should be the...
-
Describe how the following three subjects are interrelated:(give an example) a. Capital structure b. Leverage c. Risk
-
Proponents argue that HFT aids our markets by providing increased. What is one counter-argument to this claim? If we desire to thwart HFT, what is one legislative move that we can do to get them out...
Study smarter with the SolutionInn App