函數(shù)單調(diào)性及其應(yīng)用
Monotonic function and its application

摘要 函數(shù)單調(diào)性是函數(shù)的重要性質(zhì)之一，我們可以通過利用函數(shù)單調(diào)性解決許多復(fù)雜的問題，本文通過對國內(nèi)外文獻(xiàn)的查閱，希望能對函數(shù)單調(diào)性解題給出系統(tǒng)的、綜合的整合，給其他學(xué)生方便。本文第一章主要介紹函數(shù)單調(diào)性的定義及對定義的理解，第二章主要介紹函數(shù)單調(diào)性的判別方法,第三章主要介紹函數(shù)單調(diào)性在解題中的應(yīng)用,第四章主要介紹函數(shù)單調(diào)性在現(xiàn)實(shí)中的應(yīng)用，希望通過這些介紹能幫助學(xué)生更好的學(xué)習(xí)函數(shù)單調(diào)性。
關(guān)鍵詞：函數(shù)單調(diào)性，判別，應(yīng)用
Monotonic function and its application
Abstract Monotonicity is an important property of function with one variable，Using this property we can solve some complicate questions. In this paper we consult a lot of domestic and foreign document literatures about monotonic function in our library. And we hope to systematic integrate those methods about using monotonicity. In the first chapter we introduce the definition of monotonic function and analysis it. In the second chapter I will give some theorems about monotonicity and the relevant solutions. The third chapter mainly introduces the application of function monotonicity in solving the problems，The fourth chapter mainly introduces the application of function monotonicity in the real world，I hope to help students learn Monotonicity batter by introducing those.
Keywords： Monotonic function, identification, application



目錄
第一章 正確理解函數(shù)單調(diào)性的定義……………………………4
1.1函數(shù)單調(diào)性的定義………………………………………………4
1.2函數(shù)單調(diào)性的意義………………………………………………5
1.3圖像理解…………………………………………………………5
1.4自變量的值是表示某區(qū)間內(nèi)任意值………………………5
1.5單調(diào)區(qū)間不能用并集表示………………………………………5
1.6單調(diào)性命題意義…………………………………………………6
第二章 函數(shù)單調(diào)性的判別方法……………………………………7
2.1定義法………………………………………………………………7
2.2圖像法………………………………………………………………7
2.3運(yùn)算法………………………………………………………………8
2.4導(dǎo)數(shù)法………………………………………………………………8
2.5利用奇、偶函數(shù)的性質(zhì)判定………………………………………9
2.6 利用反函數(shù)的關(guān)系判定……………………………………………9
2.7 利用復(fù)合函數(shù)判定…………………………………………………9
2.8作商法………………………………………………………………10
2.9 等價形式法…………………………………………………………11
第三章 函數(shù)單調(diào)性在解題中應(yīng)用……………………………………12
3.1 利用函數(shù)單調(diào)性比較兩個數(shù)大小…………………………………12
3.2 利用函數(shù)單調(diào)性證明不等式………………………………………12
3.3 利用函數(shù)單調(diào)性求參數(shù)的取值范圍………………………………14
3.4 函數(shù)單調(diào)性在解決恒成立問題中的應(yīng)用…………………………14
3.5 利用函數(shù)單調(diào)性解不等式 ………………………………………15
3.6 利用函數(shù)單調(diào)性解方程……………………………………………16
3.7 利用函數(shù)單調(diào)性求最值……………………………………………16
第四章 函數(shù)單調(diào)性在現(xiàn)實(shí)生活中應(yīng)用………………………………18
4.1 函數(shù)單調(diào)性在合理利用材料中的應(yīng)用………………………………18
4.2 函數(shù)單調(diào)性在最大利潤中的應(yīng)用……………………………………18
4.3 函數(shù)單調(diào)性在求最短路徑中的應(yīng)用…………………………………19
結(jié)論……………………………………………………………………………20
參考文…………………………………………………………………………21