摘要本文浅谈了在各个历史时期函数的发展状况,同时探索了函数单调性及其运用。函数增减性就是我们所说的函数的单调性(monotonicity)。当函数 f(x) 的自变量在其定义区间内增大(或减小)时,函数值f(x)也随着增大(或减小),则函数在次区间具有单调性。52678
数学,是研究数量、结构、变化、空间以及信息等概念的一门学科。数学史表明,重要的数学概念的产生和发展,对数学发展起着不可估量的作用,有些重要的数学概念对数学分支的产生起着奠定性的作用,函数就是这样的重要概念,在某变化过程中有两个变量x,y,按照某个对应法则,对于给定的x,有唯一确定的值y与之对应,那么y就叫做x的函数。其中x叫自变量,y叫因变量。
毕业论文关键词:函数; 自变量; 因变量; 单调性
In this paper, we discuss the development of function in each historical period, and explore the function of the. The increase or decrease of function is what we are saying (monotonicity). When the independent variable of the function f (x) increases (decreases) in its definition, the function value f (x) also increases (decreases), then the function is monotone in the second interval.
Mathematics is a subject that studies the concept of quantity, structure, change, space and information. The history of mathematics that the emergence and development of the important mathematical concepts, to the development of mathematics plays an immeasurable role, some important mathematical concepts branch of mathematics plays a role laid, the function is such an important concept, in a process of change has two variables X, y, according to a rule of correspondence, for a given value of X, only determine the value of Y and the corresponding, then y is called X function. Where x is called the independent variable, y is called the dependent variable
Keyword:functions;independent variable; dependent vatiable; monotony
目录
1.引言 3
2.什么是函数 3
2.1函数发展过程 3
2.2函数的基本性质 4
2.2.1奇偶性 4
2.2.2单调性 5
2.2.3周期性 5
3.什么是函数的单调性 6
3.1函数单调性的定义 6
3.1.1函数单调性定义的通俗解释 6
3.1.2函数单调性的数学解释 6
3.2单调性的证明 6
3.2.1作差法 7
3.2.2中值法(拉格朗日中值定理) 8
3.2.3图像法 8
3.2.4利用已知函数的单调性 8
3.2.5利用在公共定义域内的两个单调函数加、减的单调性 9
3.2.6利用函数的奇偶性 10
3.2.7函数求导 10
4.函数单调性的运用 10
4.1函数单调性比较大小 10
4.2 求函数的值域及最值 11
4.3 求函数的极值 11
4.4 证明不等式 12
4.5