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导数是研究函数性质的一个很重要的工具。其研究的范围包括:求函数的最值、求函数的极值、比较函数值的大小、确定函数的大致图像、讨论函数的单调性、求单调区间等等。在此,我们来探究如何用导数讨论函数的单调性及求函数的单调区间。一、构造函数利用导数比较大小例1已知a、b为实数,且b>a>e,其中e为自然对数的底,求证:ab>ba。分析:通过考查函数的单调性证明不等式也是常用的一
Derivatives are a very important tool to study the nature of a function. The scope of his research includes: seeking the most value of the function, finding the extremum of the function, comparing the size of the function value, determining the approximate image of the function, discussing the monotonicity of the function, finding the monotonous interval and so on. Here, we explore how to use derivatives to discuss the monotonicity of functions and find the monotonic range of functions. First, the constructor use derivatives to compare the size of Example 1 known a, b is a real number, and b> a> e, where e is the base of natural logarithms, verify: ab> ba. Analysis: It is also commonly used to prove inequalities by examining the monotonicity of functions