[Math] the intuition behind the Lagrange multiplier

Question

I know that the minimum or maximum point is achieved when the gradient in the constraint function is parallel to the gradient on the $f$ function. But why the Lambda is called the Lagrange multiplier?

Answer 1

Lagrange was the one who was first involved in calculus of variations and therefore people tend to call many things in calculus of variations after Lagrange (such as Lagrangian dynamics, Lagrange-Euler equations, Lagrange multipliers, etc...).