Funções convexas e desigualdades: uma abordagem no ensino médio
| Ano de defesa: | 2015 |
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| Autor(a) principal: | |
| Orientador(a): | |
| Banca de defesa: | |
| Tipo de documento: | Dissertação |
| Tipo de acesso: | Acesso aberto |
| Idioma: | por |
| Instituição de defesa: |
Universidade Estadual Paulista (Unesp)
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| Programa de Pós-Graduação: |
Não Informado pela instituição
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| Departamento: |
Não Informado pela instituição
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| País: |
Não Informado pela instituição
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| Palavras-chave em Português: | |
| Link de acesso: | http://hdl.handle.net/11449/127903 http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/14-09-2015/000845916.pdf |
Resumo: | This work presents the concept and applications of one real variable convex functions. The main goal is to show their use in problems involving inequalities. In this way, it was established the relationship between the arithmetic and geometric means and proved Jensen's inequality, Young's inequality, H older's inequality and Minkowski's inequality. These inequalities provide a powerful mathematical tool both in the statement as in the resolution of problem situations that occur frequently in national and international Math Olympics. We also use them in some cases of optimization. In addition, this work aims to be a theoretical framework to be used both in regular classes as in training classes for math olympics to help students who are looking for strategies to increase their performance and provide a way for teachers to expand the teaching practice in the classroom |