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Abstract(s)
A motivaĆ§Ć£o para a realizaĆ§Ć£o deste trabalho surge em primeiro lugar devido Ć grande importĆ¢ncia que um conceito tĆ£o āsimplesā, como Ć© o conceito de derivada, desempenha em grande parte nos fundamentos de todas as ciĆŖncias exatas. Sem este conceito estamos certos que a ciĆŖncia nĆ£o seria como a vemos hoje. E na verdade, estamos certos ainda que seria impossĆvel construir grande parte das teorias que conhecemos sem a introduĆ§Ć£o deste singelo conceito. Fizemos assim uma recolha em inĆŗmeros livros de forma a podermos reunir, num sĆ³ manual, os conteĆŗdos que nos parecem serem os mais importantes e adequados para uma introduĆ§Ć£o no ensino/aprendizagem do conceito.
Apresentamos detalhadamente a forma como o conceito surgiu, a definiĆ§Ć£o, os teoremas e as fĆ³rmulas de derivaĆ§Ć£o assim como as vĆ”rias utilizaƧƵes que podem ser feitas no estudo das funƧƵes.
AnalisƔmos ainda alguns manuais usados actualmente e no passado, no ensino secundƔrio, para perceber se a forma como o conceito Ʃ introduzido sofreu alteraƧƵes ao longo dos anos e se estƔ a ser feito de forma adequada.
Com este trabalho, pretendeu-se escrever um texto de apoio Ćŗtil que permitisse aos utilizadores (alunos e professores) assimilarem os conteĆŗdos relacionados com o conceito de derivada nos diferentes nĆveis de ensino onde ele Ć© ensinado.
The motivation for this work arises first because of the great importance that such a simple concept, as the concept of derivative, plays to a large extent in the foundations of all exact sciences. Without this concept we are certain that science would not be as we see it today. And indeed, we are still certain that it would be impossible to build much of the theories we know without the introduction of this simple concept. We have thus collected a number of books so that we can gather in one handbook the contents that seem to us to be the most important and appropriate for an introduction in teaching / learning the concept. We present in detail how the concept came about, the definition, theorems and derivation formulas as well as the various uses that can be made in the study of functions. We have also looked at some textbooks used today and in the past in secondary education to see if the way the concept is introduced has changed over the years and if it is being done properly. With this work, it was intended to write a useful support text that would allow users (students and teachers) to assimilate content related to the concept of derivative in the different levels of teaching where it is taught.
The motivation for this work arises first because of the great importance that such a simple concept, as the concept of derivative, plays to a large extent in the foundations of all exact sciences. Without this concept we are certain that science would not be as we see it today. And indeed, we are still certain that it would be impossible to build much of the theories we know without the introduction of this simple concept. We have thus collected a number of books so that we can gather in one handbook the contents that seem to us to be the most important and appropriate for an introduction in teaching / learning the concept. We present in detail how the concept came about, the definition, theorems and derivation formulas as well as the various uses that can be made in the study of functions. We have also looked at some textbooks used today and in the past in secondary education to see if the way the concept is introduced has changed over the years and if it is being done properly. With this work, it was intended to write a useful support text that would allow users (students and teachers) to assimilate content related to the concept of derivative in the different levels of teaching where it is taught.
Description
Keywords
AplicaƧƵes da Derivada Concavidades Derivada Ensino da Derivada Extremos Absolutos Extremos Relativos Pontos de InflexĆ£o Teorema de Cauchy Teorema de Fermat Teorema de Lagrange Teorema de Rolle