摘要函数单调性作为函数的一个重要性质，是高中数学教材中非常重要的一部分。它是学生学习不等式、数列、解析几何等知识的重要基础。但是，函数是个复杂、抽象的东西，加上学生不成熟的思维发展和教师无法很好的把握函数解题应用，给学生学习函数的单调性带来了许多困难。因此，加强对函数单调性应用的探究是非常有必要的,这对中学函数单调性的教学有一定的促进作用。51935

针对这一问题，本课题在研究函数单调性的概念和定义的基础上，主要介绍了函数单调性的性质、定理和判断方法，深入研究函数单调性在数学领域中的应用，再联系实际生活，举例分析函数单调性在解决实际问题中的重要作用，从而系统地归纳和罗列函数单调性的应用[9]。

Functional monotonicity as a function of an important nature is an extremely important part of the current high school mathematics teaching materials. It is an important foundation for students to learn the knowledge of  inequality, series, and analytic geometry. However, because of the complexity of the function of knowledge itself, abstract and developing students' thinking ability is not mature and teachers to grasp the function problem solving teaching does not reach the designated position, which bring many difficulties to students’ learning. Therefore, it is necessary to strengthen the study of the monotonic nature of functions with applications. What’s more, it has a certain role in promoting functional monotonic of the middle school teaching.

To solve this problem, the paper is on the basic of studying the concept and definition of the monotonic function. It mainly introduces the some properties of monotone function and discriminant method, and it is in-depth study the monotonic nature of functions in the field of mathematics application. Then with practice, the paper analyses the monotone functions that plays an important role in solving practical problems by the way of example. So,the application of the relevant monotonic function is systematically summarized and listed[9].

毕业论文关键词：函数单调性；概念；判别；应用

Keyword: Monotonic function；Concept；Distinguish；Application

目    录

1 引言 5

1.1 研究背景 5

1.2 国内外研究现状 5

1.3 研究思路和方法 5

2 函数单调性的基本理念 5

2.1 函数单调性的基本概念 5

2.1.1 函数单调性的定义 5

2.1.2 函数单调性的几何理解 6

2.2 函数单调性的基本性质 6

2.3 函数单调性的常用定理 7

2.4 函数单调性的意义 7

3 判断函数单调性的方法 8

3.1 定义法 8

3.2 直接判断法 10

3.2.1 一次函数 10

3.2.2 二次函数 10

3.2.3 反比例函数 10

3.2.4 指数函数 10

3.2.5 对数函数 10

3.2.6 三角函数 11

3.3 换元法 11

3.4 导数法 11

3.5 复合函数法