## 基于MATLAB的函数性态及其应用研究

Title    Research on the properties of functions and its applications based on MATLAB
Abstract
The properties of functions are an important research topic in the calculus and have many applications. However, it is hard to find out the properties of some functions. Moreover, the image of the function can not be drawn easily. We can use the MATLAB software to solve these problems.
In this paper, we research the properties of functions including monotony, extreme points, convexity, inflection, and asymptotic. We also research how to study the properties of functions by using numerical computing, graphics and visualization capabilities of MATLAB. In fact, we can create the image of function accurately by controlling linear, plane, color, light, perspective and other attributes in the MATLAB. It display the properties of functions perfectly. This helps us solve many mathematician problems efficiently. In fact, it can achieve maximum results with little effort.

Keyword  the properties of functions,   MATLAB,   symbolic-graphic combination

1 绪论     1
1.1 研究背景    1
1.2 研究概况    1
1.3 本文的主要工作    2
2 函数的性态    3
2.1 单调性    3
2.1.1 一元函数的单调性    3
2.1.2 二元函数的单调性    3
2.2 函数的极值    4
2.2.1 一元函数的极值    4
2.2.2 多元函数的极值    5
2.3 函数的凸凹性    5
2.4 函数的拐点    6
2.5 曲线的渐近线    7
3 MATLAB简介    8
3.1 MATLAB主要部分介绍    8
3.2 MATLAB功能和特点    8
3.3 MATLAB基本操作简介    9
4 MATLAB平台下的函数性态分析    12
4.1 MATLAB求函数的导数和极限    12
4.1.1 MATLAB求函数的导数    12
4.1.2 MATLAB求函数的极限    12
4.2 MATLAB计算的可视化    13
4.2.1 二维曲线的绘制    13
4.2.2 三维图形绘制    15
4.3 利用MATLAB求函数的单调性    18
4.4 利用MATLAB求函数的极值    21
4.4.1 一元函数极值的求法    21
4.4.2 二元函数的极值的求法    23
4.5 利用MATLAB求函数凸凹性与函数的拐点    27
4.6 利用MATLAB求函数的渐近线    29
5 利用MATLAB研究函数性态举例    31

1  绪论
1.1  研究背景

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