How to Correctly Answer 'Is the Optimal Critical Point a Local Minimizer?' in Calculus Courses

Autor/inn/en	Ribeiro, Ademir Alves; Barbosa, José Renato Ramos
Titel	How to Correctly Answer 'Is the Optimal Critical Point a Local Minimizer?' in Calculus Courses
Quelle	In: International Journal of Mathematical Education in Science and Technology, 53 (2022) 6, S.1664-1675 (12 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2021.1903108
Schlagwörter	Calculus; Mathematics Instruction; Undergraduate Students; Teaching Methods + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Teaching method; Lehrmethode; Unterrichtsmethode
Abstract	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'. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01