Rolle Theorem and Applications

Mean Value Theorem,a very important in mathematical analysis,fundamental theorem in mathematical analysis has a wide range of applications.It functions a bridge between the derivative of the function,which is applied at a point in a range of local properties and the overall nature of the important tools.Using the differential equation in the mean value theorem can be proved the existence of the root of the problem,the number of all roots of the problem and the root problem of the existence interval,a number often used to prove that the equation with derivative.In the form of structure,Rolle theorem is the basis of the mean value theorem,on the one hand it contains among the mean value theorem in the other,on the other hand other proof of the mean value theorem is often achieved through the Rolle theorem,but the theorem requiring the independent variable range is a closed interval,which makes some of the problems limited.In this paper,the Rolle theorem and the open interval are infinite interval,proved by two methods,and examples of its application.