中學(xué)數(shù)學(xué)中輔助函數(shù)的構(gòu)造

摘要 構(gòu)造輔助函數(shù)法是一種通過構(gòu)造一個函數(shù)來概括題目中量與量之間的關(guān)系，利用已知條件將求未知結(jié)論轉(zhuǎn)換為求輔助函數(shù)的性質(zhì)，從而幫助解決數(shù)學(xué)問題，它在數(shù)學(xué)學(xué)習(xí)中到處可見。因而，構(gòu)造輔助函數(shù)法是中學(xué)數(shù)學(xué)學(xué)習(xí)的關(guān)鍵。
本文將討論中學(xué)數(shù)學(xué)中構(gòu)造輔助函數(shù)的意義，列舉出各種構(gòu)造輔助函數(shù)的方法，以及輔助函數(shù)在中學(xué)數(shù)學(xué)中的應(yīng)用中，輔以例題展開討論，從而讓學(xué)生對構(gòu)造輔助函數(shù)這一方法有更系統(tǒng)的認(rèn)識，更加清晰地了解并運(yùn)用。
數(shù)學(xué)構(gòu)造法本身是一個較高的數(shù)學(xué)思維活動，它往往與創(chuàng)造性、創(chuàng)新性聯(lián)系在一起，因此，通過對構(gòu)造輔助函數(shù)的研究來達(dá)到指導(dǎo)中學(xué)數(shù)學(xué)的教學(xué)，幫助學(xué)生更加熟練地運(yùn)用這一方法解題，提高解題能力，并且不僅充分說明了構(gòu)造輔助函數(shù)法在中學(xué)數(shù)學(xué)中的重要性，同時(shí)，更希望能透過構(gòu)造輔助函數(shù)法這一種數(shù)學(xué)學(xué)習(xí)的方法，進(jìn)一步培養(yǎng)學(xué)生的創(chuàng)新意識，鍛煉學(xué)生思維的開闊性與靈活性，強(qiáng)調(diào)獨(dú)立思考的重要性。

關(guān)鍵詞：構(gòu)造法 輔助函數(shù) 應(yīng)用


Construction of auxiliary function in middle school mathematics
Abstract Construct an auxiliary function method is to summarize the relationship between the amount of the amount of the title by constructing a function, using the known conditions for the sake of seeking the unknown helper function to convert the conclusion of nature to help solve mathematical problems, which in mathematics learning everywhere. Thus, constructing auxiliary function method is the key to high school math learning.
This article will discuss the significance of the method of constructing auxiliary middle school math functions, lists a variety of constructing auxiliary functions and auxiliary functions in mathematics in high school, supplemented by examples discussion, allowing students to construct the auxiliary function of this method more systematic understanding more clearly understand and use.
The mathematical construction method is a higher mathematical thinking activity, which is often associated with creativity, innovation together, therefore, through the study of constructing auxiliary functions to achieve high school mathematics teaching guide to help students be more proficient in the use of this method problem solving , improve problem-solving ability, and not fully illustrate the importance of constructing auxiliary function method in high school mathematics, while also hoping to emphasize the importance of thinking through constructing auxiliary function method which a mathematical learning, students sense of innovation, broad thinking exercises and flexibility.
Key words construction method auxiliary function application


目 錄
引 言 1
第一章 構(gòu)造輔助函數(shù)的意義 2
1.1 構(gòu)造法 2
1.2 輔助函數(shù) 3
1.3 構(gòu)造輔助函數(shù)的意義 3
第二章 構(gòu)造輔助函數(shù)的方法 5
2.1 直觀構(gòu)造輔助函數(shù)法 5
2.2 逆向思維構(gòu)造輔助函數(shù)法 6
2.3從幾何意義構(gòu)造輔助函數(shù) 7
2.4 分離參數(shù)法構(gòu)造輔助函數(shù) 8
2.5 原函數(shù)法構(gòu)造輔助函數(shù) 8
第三章 構(gòu)造輔助函數(shù)的應(yīng)用 11
3.1 構(gòu)造輔助函數(shù)證明不等式 11
3.1.1構(gòu)造差函數(shù) 11
3.1.2構(gòu)造商函數(shù) 12
3.1.3構(gòu)造對數(shù)函數(shù) 12
3.2 構(gòu)造輔助函數(shù)證明等式 13
3.3 構(gòu)造輔助函數(shù)法求值 14
3.3.1求三角函數(shù)的值 14
3.3.2求一般代數(shù)式的值 15
3.4 構(gòu)造輔助函數(shù)法求參數(shù)（或變量）的值 15
3.4.1構(gòu)造一次函數(shù) 15
3.4.2構(gòu)造二次函數(shù) 16
3.4.3構(gòu)造分式函數(shù) 16
3.4.4 構(gòu)造指數(shù)函數(shù)求參數(shù)的范圍 17
3.5 輔助函數(shù)在數(shù)列中的運(yùn)用 18
3.5.1 直接構(gòu)造輔助函數(shù)解數(shù)列問題 18
3.5.2 構(gòu)造輔助函數(shù)求導(dǎo)解數(shù)列問題 19
結(jié)論 21
致謝 22
參考文獻(xiàn)： 23