[分析] 均值定理
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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