The Graphic Derivation Process of Lagrange Multiplier Method

The Lagrange multiplier method is an effective method for finding the extreme values of functions, which can solve some complex mathematical and engineering problems. The introduction of this method in the textbook is only a simple expression, but it does not explain how this expression is derived. This article provides a detailed derivation of the Lagrangian multiplier method expression through graphical methods combined with the gradient principle. The Lagrange multiplier method has important applications in various engineering methods, and one of the closely related applications is the gradient descent method. Therefore, after understanding the working principle of the Lagrange multiplier method, one can deepen their understanding and mastery of related issues in the subsequent learning process.