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课题:函数单调性适用年级:高三年级学期:2006～2007学年度第一学期要点提示函数的单调性是历年来高考的重点内容之一,考查内容灵活多样．函数的单调性是比较大小、解不等式、求函敷极值(或最值)或代数式取值范围的主要依据,其应用较为广泛与灵活．复习过程中要理解单调性定义,正确认识单调函数图像,掌握解题方法,学会用性质解题．对于探求函数的单调区间或判断函数的单调性方面问题的处理,一方面考虑从定义出发用定义解之,这种方法运算量大且遇到复合函数问题时,既要掌握基本函数又要把握复合过程,思维过程比较复杂,另一方面应重点掌握用导数方法探求函数的单调区间及应用函数单调问题,同时也要注意结合函数的图像加强数形结合思想在解题中的作用．
Topic: Functional monotonicity Applicable Grade: Grade 3 Semester: 2006-2007 First semester Key Points Tip The monotonicity of the function is one of the key contents of the college entrance examination over the years. The contents of the examination are flexible and diverse. The monotonicity of functions is the main basis for comparing size, solving inequality, finding the extremum (or the maximum value) or algebraic range, and its application is more extensive and flexible. During the review process, we must understand the definition of monotony, correctly understand the monotonous function image, master the problem solving method, and learn to use the nature to solve the problem. To explore the monotonicity of functions or to determine the monotonicity of functions, on the one hand, consider starting from the definition and using the definition to solve the problem. This method requires a large amount of calculations and encounters compound functions. The complex process and thinking process are more complex. On the other hand, we should focus on the use of derivative methods to explore the monotonic range of functions and the monotonic problem of applied functions. We must also pay attention to the role of the image-strengthening number-associative combination method in solving problems.