Lagrange Multiplier Calculator
Find extrema of functions subject to constraints using the method of Lagrange multipliers.
Lagrange Multiplier Calculator
Find extrema of functions subject to constraints
Function Parameters
Lagrange Multipliers
The method of Lagrange multipliers finds the extrema of a function f(x,y) subject to a constraint g(x,y) = 0 by solving:
∇f = λ∇g
g(x,y) = 0
Where λ is the Lagrange multiplier. Solutions to this system give critical points that may be maxima, minima, or saddle points.
Results
Your Lagrange multiplier solutions will appear here
Common Examples
| Function | Constraint | Solution |
|---|---|---|
| x² + y² | x + y = 2 | (1,1), λ=2 |
| xy | x² + y² = 1 | (±√0.5,±√0.5), λ=±0.5 |
| x + 2y | x² + y² = 4 | (1/√5, 2/√5), λ=√5/4 |
| x²y | x² + 2y² = 6 | (2,1), λ=1 |
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Understand the Lagrange multiplier method step-by-step
Enter Your Functions
Input your objective function and constraint equation
Calculate Critical Points
The calculator solves ∇f = λ∇g with g=0
Get Solutions
View critical points with function values and λ
Key Features
What makes our Lagrange Multiplier Calculator special!
Multiple Variables
Handles functions of two variables (x and y)
Common Examples
Includes template problems for quick testing
Step Explanations
Explains the mathematical method being used
Who Can Benefit
Our Lagrange Multiplier Calculator helps various users:
Calculus Students
Learn constrained optimization techniques
Math Teachers
Demonstrate optimization problems visually
Engineers
Solve real-world constrained optimization problems
Researchers
Quickly test optimization scenarios
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Try NowUser Reviews
Rated Excellent 4.98/5 on There's An AI For That (TAAFT) - The #1 AI Aggregator
- Jun 17, 2025
Saved My Calculus Grade!
This calculator helped me understand Lagrange multipliers for my exam.
Emily R.Verified Review - Jun 15, 2025
Professor Approved
I use this tool to demonstrate optimization concepts in my classes.
Dr. Johnson, MathematicsVerified Review - Jun 13, 2025
Engineering Essential
Perfect for solving constrained optimization problems in my work.
Michael B.Verified Review - Jun 11, 2025
Clear Explanations
The method explanation helped me grasp the concept better.
Sophia L.Verified Review
Frequently Asked Questions
Is this Lagrange Multiplier Calculator free?
Yes, our Lagrange Multiplier Calculator is completely free to use.
What is the method of Lagrange multipliers?
The method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equality constraints.
How many variables does this support?
This calculator currently supports functions of two variables (x and y).
Are the solutions exact?
This calculator demonstrates the concept but uses simplified calculations. For exact solutions, you would typically solve the system symbolically.
Can I copy the results?
Yes, each solution point includes a copy button to copy the values to your clipboard.
What's the difference between maxima and minima?
Maxima are the highest points (peaks) while minima are the lowest points (valleys) of a function within a given domain.
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