Math Problem Statement
function: 4x-y+2 and constraint is 2x^2 +y^2 =1
Solution
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Math Problem Analysis
Mathematical Concepts
Optimization
Lagrange Multipliers
Constrained Optimization
Formulas
Lagrange multiplier: \(\mathcal{L}(x, y, \lambda) = f(x, y) - \lambda (g(x, y) - c)\)
Partial derivatives
Solving systems of equations
Theorems
Lagrange Multiplier Theorem
Suitable Grade Level
Undergraduate (Calculus level)
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