Geometric Intuitive treatment of the Lagrange multipliers method

Abstract

Lacking of Geometry skills causes many first year calculus students to fail in understanding constrained optimization problems and methods. The usual abstract presentation of these issues do not help. Fortunately nowadays we can use software aides to improve students' performance. Our aim in this paper is to develop a learning module for the Lagrange method using free tools like Maxima and Asymptote.The module take the student through the following steps:Review of the basic geometry of curves and surfaces, implicit and parameterized.Use of Maxima or Asymptote to visualize curves and surfaces.The constrained optimization problem.Solution in the parameterized curve/surface case.Solution in the implicit curve/surface case.Use of Maxima or Asymptote to visualize solutions.