Calculus › Section N · Functions of several variables › Topic N.10
Lagrange multipliers
Sometimes the constraint you must respect makes substitution algebra a nightmare. Lagrange multipliers optimise under constraints directly, by asking one geometric question: where do the level curves touch?
In this topic
- Optimising under a constraint
- The tangency principle
- Lagrange's equations
- Worked example: the largest fenced rectangle
- What λ is telling you
- Worked example: nearest point on a hyperbola
- Three variables, same machinery
- Substitution or Lagrange?
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP