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Lagrange multiplier calculator

Most accurate and 100% Free lagrange multipliers calculator 

Lagrange Multipliers Calculator

How To Use the Lagrange Multiplier Calculator?

You have to follow some simple steps to use Lagrange multiplier calculator

Step 1: Firstly, you have to enter the values in the given text boxes.

Step 2: Enter the function in the text box

Step 3: Enter the constraints in the text box

Step 4: Choose the type of extremum option such as (min or max) you want to find.

Step 5: Press the calculate button and get the results in seconds.

What is the Lagrange multiplier?

Lagrange multiplier in mathematical optimization is a simple technique to identify the local maxima as well as minima of a function of the form f(x, y, z) Lagrange multiplier calculator with steps. The Lagrange multipliers are also known as undetermined multipliers.

The formula for the Lagrange multiplier

Mathematically how to calculate lagrange multiplier:

L (x, λ) = f(x) – λg(x)

Function: f (x1,x2,…,xn) 

Constraints: gi (x1,x2,…,xn)=0. 

The constant λ, is called the Lagrange Multiplier.

How Does the Lagrange Multiplier Calculator Work?

Reuters Provide best Lagrange multipliers calculator online. The basic functionality behind the working of this tool is, it utilizes Lagrange multiplier technique to identify the extrema points in the starting phase then calculates values of multivariate function in terms of the maxima as well as minima, subject to one or more equality constraints.

The working phenomena to find max and min using lagrange multipliers calculator is: 

1)    To calculate lagrange multiplier firstly it requires a function (which is also known as object function). The function f(x, y) must contain two variables such as x, y. 

2)   The second required element is the constraints. E.g. 6x+5y<=100

3)  The Lagrange Multiplier calculator performs calculations through the following equation to find out the maximum and minimum values to provide the exact solution.

After taking functions and constraints as input values. The above equation used to perform computations to find output (as optimized values that satisfy the constraints).

Usage of Lagrange Multipliers

The primary purpose of using the Lagrange multiplier is to deal with multivariate functions as well as this calculator supports such functions and multiple constraints.

It is also considered as a constrained optimization strategy.

This tool is useful in helping the following fields.

Lagrange multipliers method is used to solve extreme value problems in science, economics, and engineering.


Lagrange multipliers are useful in solving optimization problems in economics including profit maximization, cost minimization.


Not only limited to economics, the tool has several applications in physics such as finding path in calculus of variation to minimize or maximize certain integral.


In the field of engineering the Lagrange multipliers help engineers to optimize structural design problems.

Machine Learning: 

In the modern era of AI, the Lagrange multipliers have some applications in machine learning to optimize the ML algorithms to train models like SVM.


How do you know when to use Lagrange multipliers?

Mostly the Lagrange multipliers required when someone has to solve the optimize problem to identify the max and min of some function subject to equality constraints.

How do you know if Lagrange multipliers give maximum or minimum?

It can be recognize when satisfy the following factors:

  • The (max, min or saddle point) is determined through evaluating the objective function’s 2nd order partial derivatives under such conditions.
    • The indication or identification of a local minimum is when the positive definite Hessian matrix of a 2nd order partial derivative occurs (local minimum).
    •  Negative definite of the Hessian matrix represents the local maximum.
    • Positive as well as negative eigenvalues of Hessian’s matrix represent saddle points.

What is the working rule of our Lagrange multiplier?

The basic working functionality of Lagrange multiplier includes following steps:

  1. The object function formulation needed for optimization.
  2. Equality constraints formulation
  3. To introduce the Lagrange multiplier, establish Lagrangian via merging the function and constraints.
  4.  Construct Lagrangian partial derivatives regarding the variables such as:
  1.     actual variable
  2.     Lagrange multipliers

Which is equal to zero?

  1.  identify the critical points through resolving the equation.
  2.  Utilize the 2nd order partial derivatives to Investigate the nature of critical points.
  3. At the final stage, if it satisfies the actual equality constraints which can confirm through the Validity of outcome.


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