最近笔者通过对2006年各省市高考试题的研究发现两个不等式问题的一个新证法,并得出这两道试题的改进,进而给出此类不等式问题证明的一般规律,以飨读者.例1(陕西省2006年高考试题)已知函数f(x)=x3-x2+2x+41且存在x0∈0,21,使f(x0)=x0.(1)证明:f(x)是R上的单调增函数;(2)设x1=0, Recently, the author has found a new method of proof for the two inequality problems in the study of the examination questions of provinces and cities in 2006, and has obtained the improvement of these two questions, and then given the general law of the proof of such inequalities, in order to readers. 1 (Shaanxi Provincial Examination Exam 2006) Known function f(x)=x3-x2+2x+41 and there exists x0∈0,21 so that f(x0)=x0. (1) Proof: f(x) is Monotonically increasing function on R; (2) Let x1=0,