利用导数研究函数的单调性、极值和最值来证明不等式是函数、导数、不等式综合中的一个难点,也是近几年高考的热点.解决此类问题主要是把不等式的证明转化为利用导数研究函数的单调性或求最值,而关键是如何根据不等式的结构特征构造一个可导函数,再用导数证明不等式.现在归纳几种常见的构造函数的方法,具体如下. Using the derivatives to study the monotonicity, extreme value and the maximum value of the function to prove inequality is a difficult point in the synthesis of functions, derivatives, and inequalities, and it is also a hot spot of the college entrance examination in recent years. Solving such problems is mainly to convert the proof of inequality into the use of derivatives. To study the monotonicity of function or find the best value, and the key is how to construct a derivative function according to the structural features of inequality, and then use the derivative to prove the inequality. Now we sum up several common methods of constructor, as follows.