Lagrange multiplier Definition and 75 Threads

Let f(x,y)= -2x^2-2xy+y^2+2 Use Lagrange multipliers to find the minimum of f subject to the constraint 4x-y = 6 ∂F / ∂x =..... i got -4x-2y+2y but i coming out as wrong what am i missing ∂F/ ∂Y= ... The function f achieves its minimum, subject to the given constraint, where x =...

A rectangular solid of maximum volume is to be cut from a solid sphere of radius r. Determine the dimension of the solid so formed and its volume? I have defined my function F(l,b,h) as lbh, but i don't know how to define my constraint condition from my question

1. Problem Statement: Use Lagrange multipliers to find the volume of the largest box with faces parallel to the coordinate system that can be inscribed in the ellipsoid: 6x2 + y2 + 3z2 = 2 2. Homework Equations : f(x,y,z) = \lambdag(x,y,z) 3. Attempt at a solution f(x,y,z) is the...

Homework Statement Find the extreme values of the function f(x,y,z) = xy + z^2 in the set S:= { y\geq x, x^2+y^2+z^2=4 } Homework Equations The Attempt at a Solution Ok, so This is clearly a lagrange multiplier question. Geometrically, I can see that the region that is the constraint is...

Find the maximum value of f(x,y,z) = 5xyz subject to the constraint of [PLAIN]http://www3.wolframalpha.com/Calculate/MSP/MSP9619f6019f3fia87i60000567g3gb3dhi833if?MSPStoreType=image/gif&s=6&w=126&h=20. I know to find the partial derivatives of the function and the constraint. Then, set up...

Homework Statement Hello. I've been stuck on a Lagrange Multiplier problem. It's from Mathematical Methods in the Physical Sciences by Mary Boas 3rd edition pg. 222. The question is: What proportions will maximize the volume of a projectile in the form of a circular cylinder with one conical...

I think that many of us have had to endure working with Lagrange multipliers in the past, but it seems to me that it has always been taught incorrectly. So the statement (if you will allow me to use differential forms) is Now my issue is that it's well-known that this should be...

Homework Statement OK I have a Differential Calculus exam next week and I do not understand about Differential Manifolds. We have been given some questions to practise, but I have no idea how to do them, past a certain point. For example 1. Study if the following system defines a manifold...

Hi, Dear Math forum users, I was practicing with my optimization course problem and encountered one type of Lagrange multiplier question which I have trouble with. I am wondering if anyone could enlighten me for the following Lagrange problem. function f = x*y*z subject to 4xy+3yz+2xz...

Homework Statement I am doing this lagrange multiplier problem with 2 constraints. I have completely solved it as shown in the image below. I have found that for lambda = 1 and mu = +/- 1/2 I have that x=+/- [sqrt(2)] y=+/- [1/sqrt(2)] and z=+/- [1/sqrt(2)]. So I am trying to figure...

Homework Statement Find the points on the level surface xy2z4=1 that are closest to the origin. Homework Equations Lagrange's method for finding extrema The Attempt at a Solution If I have a level surface F(x,y,z)=c, it's points closest to the origin will be the ones in which...

Find an equation of the largest sphere that passes through the point (-1,1,4) and is such that each of the points (x,y,z) inside the sphere satisfies the condition x^2 + y^2 + z^2 < 136 + 2(x + 2y + 3z) I know this problem requires Lagrange multipliers. I assume that x^2 + y^2 + z^2 is...

I have a problem where I'd like to minimize a certain function subject to the constraint that a related function is at a maximum, that is I have a function F(a,b) I would like to know what its minimum is when G(a,b) is at a maximum. I'm not sure how to set this problem up, I know that for the...

Homework Statement Use the Lagrange Multiplier method to find the maximum and minimum values of x2 − 2xy + 7y2 on the ellipse x2 + 4y2 = 1. Homework Equations Lagrange multiplier method The Attempt at a Solution L(x,y,z,λ) = x2 − 2xy + 7y2 - λ(x2 + 4y2 - 1) Find Lx, Ly, Lλ Then, solve for x...

Homework Statement A window of fixed perimeter is in the shape of a rectangle surmounted by a semi-circle. Prove that its area is greatest when its breadth equals its greatest height. Homework Equations SA = lw + (pi*l^2)/4 <--- Thats what I got the surface area to be. Perimeter = 2w +...

ok this is just an example so you can see where I am having problems with these(it isn't hw) i need to find the optimum values of X and Y U= XY m= Psuby(Y) + Psubx(X) the first order conditions are Y +u*Psubx X+ u*PsubY m= Psuby(Y) + Psubx(X) now , where I am having...

Use Lagrange Multipliers to find the maximum and minimum values of f(x,y)=x^{2}y subject to the constraint g(x,y)=x^{2}+y^{2}=1. \nablaf=\lambda\nablag \nablaf=<2xy,x^{2}> \nablag=<2x,2y> 1: 2xy=2x\lambda ends up being y=\lambda 2: x^{2}=2y\lambda ends up being(1...

How to solve this problem? : Consider two particles of masses m1 and m2. Let m1 be confined to move on a circle of radius a in the z = 0 plane, centered at x = y = 0. Let m2 be confined to move on a circle of radius b in the z = c plane, centered at x = v = 0. A light (massless) spring of...

Hey guys! I have been on the forum for about a week or so and have compiled a lot of information and techniques to help me understand calculus, so i really appreciate everyone's help! I am a soon-to-be freshman in college and am taking a summer class, calculus II (took calc I in HS). This is...

Hi, Why is -BEi used instead of +BEi as the lagrange multiplier for indistinguishable particles? How is it justified? I've been reading a book about statistical mechanics and it introduces lagrange multipliers first for distinguishable particles- it has ln(ni) + a + BEi = 0. (where a is...

Question: Use Lagrange multiplier method to determine the point on the curve y=1-x^2 that maximises the function f(x,y)=2x + y. Hence find the maximum value of f. Attempt at Solution: Okay I used the Lagrange method to get a point on the curve and I got (1,0) How do I find the...

Hi, I would appreciate if anyone can help me out with the following question. I've been asked to find the point on the surface z = xy + 1 nearest to the origin by using the Lagrange Multiplier method. But all the examples I've been given in class and for coursework gave you the constraint...

This problem was given in my calc class during the semester, "Find the lowest point on the intersection of the sphere x^2+y^2 +z^2 = 30 and the cone 2*x^2 +y^2 = c^2". I don't know how to solve this problem with lagrange multipliers. How is it done? Thanks! Callisto

Hey guys, i need some help with this problem. It goes as follow: Find the global max and min valves of the fuction z=x^2+2y^2 on the circle x^2+y^2=1. Ok and here is what i have done. I found the derivites and have done (K is the lagrange constant) 2x=2xK K=1 4y=2yK K=2 Then i set...

Find the points at which the function f(x,y,z)=x^8+y^8+z^8 achieves its minimum on the surface x^4+y^4+z^4=4. I know 8x^7=(lamda)4x^3 8y^7=(lamda)4y^3 8z^7=(lamda)4z^3 x^4+y^4+z^4=4 Case1: x not equal to 0, y not equal to 0, and z not equal to 0 I get 3(4th root of 4/3 to the eigth)...