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不等式证明是高中数学的重点难点之一.不等式的种类繁多,证明的方法也难易悬殊,使用的技巧各异,尽管教材中对不等式的证明给出了系统的总结,但是有很多不等式,我们还是较难快速简洁地证明它.特别是有些不等式,如果用常用的初等方法去证明,我们会感到无从下手.这时如果我们如果将它作个恒等变形,使它转化为我们较熟悉的函数不等式,再借助导数,利用函数的相关性质来证明,往往会事半功倍.一、利用函数单调性证明不等式
Inequality proves to be one of the most important and difficult points in high school mathematics.With a great variety of inequalities, the methods of proof are also difficult to be distinguished and the skills used are different. Although the proofs of inequalities in the textbook give a systematic summary, there are many inequalities that we It is hard to prove it quickly and succinctly, especially if there are some inequalities that we can not start with if we use the usual elementary methods to prove that we would transform it into something we are more familiar with Function inequality, and then by means of derivatives, the use of related properties of the function to prove that often will do more with less. First, the use of monotonicity to prove inequalities