EDB — 1H8

[1H8] Prerequisites:[1F6]↺↻,[1H1]↺↻. Let \(f,𝜑\) be class \(C^ 1\) in the open set \(A\), and let \(\overline x\) be a local minimum point for \(f\) bound to \(E_ a\) (so \(𝜑(x)=a\)). Show that \(𝜆∈ℝ\) exists such that \(∇ f(\overline x)+𝜆 ∇𝜑(\overline x)=0\); this \(𝜆\) is called the Lagrange multiplier.