IB Math HL IA_Quartics (7점)

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본 문서는 2022년 작성한 IB Math 중 Properties of quartics를 주제로 잡은 IA 입니다.
7점 받았기에, 도움 많이 되시리라 생각합니다.

 

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Introduction

During learning the IB math course, one of the most familiar mathematical concepts of functions were linear and quadratic functions. However, there is some limited information about higher degree functions such as third-degree and fourth-degree functions. Those functions are slightly covered with differentiations and general ideas of functions named as polynomial functions, but I was not able to have a chance to explore their mathematical patterns and features in-depth such as properties regarding each vertex, inflection points, and so on. While I was exploring higher degree functions, I found out quartic functions which looked like double quadratic functions – two quadratic functions connected with each other. I wondered if quartic functions would have similar properties with quadratic functions or have distinct properties unlike linear or quadratic functions.

Thus, I came up with a research question, “To what extent does the quartic function have unique properties in terms of mathematics?”.

Based on this curiosity, I decided to investigate properties of quartics with more details. I set a random quartic function, (), so by using differentiation, I would be able to find the inflection point of the functions, labelling them as and . I am going to make an equation with the two giving points of inflections, following up with the other two points where linear line and quartic function meets. So, I am going to label them as and . Thus, I would like to analyze the relationship among four points. During this progress, I am going to use mathematical tools that I learned during the IB math course – differentiation, integration, functional properties, and basic mathematical knowledge regarding functions.

Thus, I aim to understand new mathematical concepts, quartic functions, and furthermore to investigate properties of quartics. I expect that this investigation can improve my own understanding of the function itself and I can extend my mathematical knowledge of linear and quadratic functions to quartic functions…

 

  • 총 페이지수: 23 pages
  • 과목명: Mathematics
  • 주제: To what extent does the quartic function have unique properties in terms of mathematics?
  • The file is in PDF format.
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IB Math HL IA_Quartics (7점)

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