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教学目的:1.理解函数单调性概念,掌握判断函数单调性的方法,会证明一些简单函数在某个区间上的单调性,体验用数学语言刻画函数单调性的必要性。2.经历函数单调性的探究过程,体验数学语言的准确简洁之美。教学重点:函数单调性的概念与判断及证明。教学难点:函数单调性概念的形成;运用定义证明函数的单调性。教学过程:一、问题情境问题:观察图像,说出气温在哪些时间段内是升高的?怎样用数学语言刻画“一定时段内,随着时间的推移气温逐步升高”这一特征?
Teaching Objectives: 1. To understand the concept of monotonicity and to master the monotonicity of a function, we will prove the monotony of some simple functions in a certain interval, and experience the necessity of using mathematical language to characterize monotonicity of functions. 2. Experiencing monotonic nature of the process of inquiry, to experience the exact concise beauty of mathematical language. Teaching focus: the concept of monotonicity and judgment and proof. Difficulties in teaching: the formation of the monotonic function concept; the use of definitions to prove the monotonicity of the function. Teaching process: First, the problem situation problems: observe the image, say the temperature is raised in what time? How to use mathematical language to describe “within a certain period of time, as time goes by temperature gradually ” this feature ?