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导数是高中数学新教材与新课标中新增的知识之一,体现了近代数学思想,在研究函数性质时,有其独到之处.高考试题中,大多数以一个大题的形式考查这部分内容,内容主要与单调性、最值、切线三方面有关.高考更重视函数与导数的结合,利用导数判定一些函数的单调性、求函数的极值和最值,这是研究函数性质的强有力的工具.下面以导函数的类型为切入点对导数题型分类如下.一、导函数为一次函数类型例1已知函数f(x)=ax-lnx,是否存在实数a,当x∈(0,e](e是自然对数的底数)时,函数f(x)的最小值是3?若存
The derivative is one of the new knowledge in the new high school mathematics textbook and the new curriculum standard. It embodies the modern mathematics thought and has its own uniqueness in the study of the nature of the function. Most of the high exam questions are examined in the form of a big question. Part of the content, the content is mainly related to the monotonous, the most value, tangent three aspects. College entrance examination more emphasis on the combination of function and derivative, the use of derivative to determine the monotonicity of some functions, find the function of the extreme and the maximum value, which is to study the nature of the function Powerful tools. The following types of derivatives are used as entry points. The derivative questions are categorized as follows. First, the derivative is a function type. Example 1 Known function f(x) = ax-lnx, if there is a real number a, when x When ∈(0,e)(e is the base of the natural logarithm), the minimum value of the function f(x) is 3?