导数作为高中新教材新增加的教学内容,其工具性作用日益明显,在高考中的地位也更加突出,尤其是导数与不等式结合的综合问题的考查,已成为近年各地高考的一个热点.以下面举几个例子,说明利用导数证明不等式的一般方法.例1(07年安徽)设a≥0,求证:当x1时恒有xln2x-2alnx+1.证明 Derivatives as a new teaching content of new high school textbooks, the instrumental role of the increasingly obvious, the status of the college entrance examination is also more prominent, especially the integration of derivatives and inequality test has become a hot spot around the entrance examination in recent years. To give a few examples, illustrate the general method of using derivatives to prove inequalities. Example 1 (Anhui Province in 2007) Let a ≥ 0, and prove: x1n2x-2alnx + 1 when x1.