利用单调性与极限判断函数的正负性

Using Monotonicity and Limit to Judge thePositive and Negative of a Function

摘要: 本文主要研究在区间（a, b）上的可导函数f(x)的正负性问题(a, b可以为无穷)。借助于函数的单调性和在端点处的极限值与零的大小关系，推导出了判断函数f(x)在区间（a, b）上的正负性的三个充分条件，最后通过三个例题表明用本文的结论可以更加简便地证明一些具体问题。

Abstract: In this paper, the positive and negative problems (a, b can be infinite) of the derivative function f(x) on the interval (a, b) are studied. By using the monotonicity of the function and the relationship between the limit value and the zero at the end point, three sufficient conditions for the positive and negative properties of the judgment function f(x) on the interval (a, b) are deduced, and finally through the three examples to show that the conclusion of this paper can be used to prove some specific problems more easily.