[分析] 均值定理

[rebe212296 (綠豆冰)]

均值定理for Derivatives

Assume that f has a derivatives(finite or infinite) at each point of an open

interval (a,b), and assume also that f is continuous at both

endpoints a and b.

Then there is a point c in (a,b) such that f(b)-f(a)=f'(c)(b-a).


均值定理for Differentiable functions

Let S be an open subset of R^n and assume that f:S→R^m is differentiable

at each point of S.

Let x and y be two points in S such that http://ppt.cc/hSwk .

Then for every vector a in R^m threr is a point z in L(x,y)

such taht a*{f(y)-f(x)}=a*{f'(z)(y-x)}.


請問均值定理for Differentiable functions, 為什麼前提函數不用要求連續?

謝謝!

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