摘  要: 极值和最值问题是数学中常见的一类问题，是高考中的热点考点，同时在科学与生产生活实践中存在着许多和极值、最值相关的问题. 对于极值与最值在实际问题中的求解，将有利于培养学生认真严谨的思维能力，有利于培养学生灵活运用知识的能力，有利于培养学生自觉处理问题的习惯. 极值与最值问题涉及到几何、代数、微积分、变分法、规划论、组合数学等数学分支的知识，有一定的难度.66626

    本文以近几年全国各省市高考理科试卷为例，对极值和最值问题的解法进行一些有益的总结. 探讨如何求解这类问题、以及对试卷中常见错误的解决提供一些策略思考，以期对提高这部分内容的教学质量有所帮助.

毕业论文关键词：定义域；导数；最值；函数单调性；极值

Abstract: The extreme value and maximum-minimum problem is a common problem in mathematics, is a hot point in the college entrance examination at the same time, a great numer lot of the extreme value, and maximum-minimum related problems in the science and the practice of production and living. For extreme value and the solution in practical problems, there will be conducive to the cultivation of thinking ability of students serious, is conducive to the cultivation of students the flexibility to use knowledge ability, is conducive to the habit of cultivating the students' consciousness of dealing with problems. The extreme value and maximum-minimum problem involves geometry, algebra, calculus, variational method, programming theory, combinatorics and other branches of mathematics knowledge, have some degree of difficulty. 

 In this paper, in recent years the various provinces and cities nationwide college entrance examination for the solution of the most cases, the extreme value and maximum-minimum problem for some useful conclusion. To explore how to solve this problem, and to solve the common errors in papers provide some strategies, in order to improve the teaching quality of this part of the help.

Keywords: Domain of definition; Derivatives; maximum-minimum; The monotonicity of the function; Extreme value   

目  录

1  引言 4

2  函数极值与最值两者间的关系 4

2.1 最值与极值的定义 4

2.2  最值与极值的关系 4

3  极值的判定法则 6

4  高考数学中常见最值问题的求法 7

4.1  判别式法 8

4.2  换元法 8

4.3  函数单调法 8

4.4 配方法 9

4.5  导数法 10

4.6  消元法 10

4.7 不等式法 11

4.8  数形结合法 12

5  求函数的极值与最值解法的误点及分析 12

5.1  配方法 12

5.2  判别式法 14

5.3  平均值法 15

结  论 17

参考文献 18

致谢 19

1  引言

极值与最值问题是中学数学经典理论的课程，是微积分应用中的一个重要内容，也是解决数学问题和实际问题的强有力工具之一. 它可帮助学生提高自身的数学素质，并且引导他们多层次、多方位选择不同的途径去解决问题. 同时，随着数学的发展，极值与最值在自然科学、社会科学与工程技术的各个领域都有着广泛的应用.