题目

请问Rolle中值定理和Lagrange中值定理的英语翻译是什么?

提问时间：2021-03-19

答案

Rolle's theorem:
If a real-valued function f is continuous on a closed interval [a,b],differentiable on the open interval (a,b),and f(a) = f(b),then there is some real number c in the open interval (a,b) such that f'(c)=0.
lagrange mean value theorem:
Let f :[a,b] → R be a continuous function on the closed interval [a,b],and differentiable on the open interval (a,b),where a < b.Then there exists some c in (a,b) such that f'(c) = (f(b)-f(a))/(b-a).
The mean value theorem is a generalization of Rolle's theorem,which assumes f(a) = f(b),so that the right-hand side above is zero.