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Lagrange Multiplier Calculator Guide
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- Purpose and Functionality
- Calculator finds maxima and minima of multivariate functions with equality constraints
- Supports both single and multiple constraints in various forms
- Results include 3D graphs and contour plots for two-variable functions
- Calculator Interface
- Offers three options: Maximum, Minimum, or Both
- Requires function and constraint input in separate text boxes
- Supports both maximum and minimum calculations
- Working Principle
- Uses Lagrange multiplier method to find extrema points
- Solves equations for single or multiple constraints
- Identifies points where function derivatives are zero
- Example Application
- Calculates maximum of xy+1 subject to x^2+y^2=1 constraint
- Solves system of three equations for lambda
- Determines four possible extrema points
- Calculates function values at extrema points to determine extrema type