How to correctly answer ‘Is the optimal critical point a local minimizer?’ in Calculus courses
-
Ademir Alves Ribeiro [1] ; José Renato Ramos Barbosa [1]
-
[1] Universidade Federal do Paraná
Universidade Federal do Paraná
Brasil
-
- Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 53, Nº. 6, 2022, págs. 1664-1675
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
-
Resumen
This short note discusses how the optimality conditions for minimizing a multivariate function subject to equality constraints have been covered in some undergraduate Calculus courses. In particular, we will focus on the most common optimization problems in Calculus of several variables: the 2 and 3-dimensional cases. So, along with sufficient conditions for a critical point to be a local minimizer, we also present and discuss counterexamples for some statements that can be found in the literature of undergraduate Calculus related to Lagrange Multipliers, such as ‘between the critical points, the ones which have the smallest image (under the function) are minimizers’ or ‘a single critical point (which is a local minimizer) is a global minimizer’.
