Lagrange Multipliers Theorem

This lecture covers the Lagrange Multipliers Theorem, focusing on the cases n=2 and the general case. It explains the necessary conditions for extrema linked to the Lagrange multipliers method. The slides illustrate the method step by step, showing how to find extrema under constraints and the geometric interpretation of the Lagrange multipliers. The lecture also discusses linear independence, vector spaces, and finding extrema of functions under constraints. It concludes with practical examples of finding extrema on spheres and the application of Lagrange multipliers.