Suddenly, a constraint is introduced. Perhaps there is a specific winding road, a river, or a property line you must stay within. Let’s call this path $g(x, y) = c$.
This gives us the central equation of the story: $$ \nabla f = \lambda \nabla g $$ paul's online math notes lagrange multipliers
∇f(x,y,z)=λ∇g(x,y,z)nabla f of open paren x comma y comma z close paren equals lambda nabla g of open paren x comma y comma z close paren Suddenly, a constraint is introduced