11条件命题+=2的证明及推广1/f′（ξ1）+1/f′（ξ2）=2

利用介值定理和拉格朗日中值定理证明了命题：设函数f(x)在0,1]上连续,在(0,1)内可导,且f ′(x)>0, f(0)=0, f(1)=1,则存在ξ1,ξ2∈(0,1),使得1/f′(ξ1)+1/f′(ξ2)=2。通过对命题证明过程的分析,对命题进行了推广。

1 1 Proof and generalization of the proposition 1/f′(ξ1)+1/f′(ξ2)=2

A proposition is proven applied with intermediate value theorem and Lagrange mean value theorem:set the function f(x) in the interval 0, 1] is continuous, when this function is derivable in the interval (0, 1), meanwhile f ′(x) > 0, f(0) = 0, f(1) = 1, then there exists ξ1 , ξ2 ∈ (0, 1) to ensure 1/f ′(ξ1 ) + 1/f ′(ξ2 ) = 2. Through the proposition’s proof process, the proof problem’s generalization is gained.