# Lagrangian multipliers

Not what you're looking for?

Use Lagrangian multipliers to find the points on the ellipse with the equation x^2+xy+y^2=3 that are closest to and farthest from the origin

##### Purchase this Solution

##### Solution Summary

This shows how to use Lagrangian multipliers to find the points on the ellipse with the given characteristics.

##### Solution Preview

Well, we consider a point (x, y) on the ellipse. Its distance to the origion would be x^2+y^2. Therefore, we want to optimize x^2+y^2 with respect to the constraint: x^2+ xy+ y^2= 3 or x^2+ xy+ y^2- 3= 0 which is the equation of the given ellipse. Let's define p to be the lagrange multiplier, then we will have:

F= x^2+ y^2+ p(x^2+ xy+ y^2- 3)

Now we take the derivative of F with respect to x, ya nd p respectively and put them equal to zero to find the critical points.

dF/dx= 2x+ 2px+ py= 0 (1)

dF/dy= 2y+ px+ 2py= 0 (2)

df/dp= x^2+ xy+ y^2- 3= 0 (3)

Ok, we have 3 equations. The first two equations are linear in x and y and ...

##### Purchase this Solution

##### Free BrainMass Quizzes

##### Probability Quiz

Some questions on probability

##### Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

##### Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

##### Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

##### Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.