Re: [微分] 習題...
: 5.Let f be differentiable on an open interval I.Prove that,if f'(x) = 0
: for all x in I,then f is constant on I.
[已修正]
if a<x<b for any a,b in I
由M.V.T.知 (a , b)間存在一c值 ,
使得 f'(c) = [ f(b)-f(a)] / b-a = 0
=> f(b) - f(a) = 0
=> f(x)為一定值函數
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◆ From: 140.112.128.93
※ 編輯: Qmmm 來自: 140.112.128.93 (11/09 20:20)
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※ 編輯: Qmmm 來自: 140.112.128.93 (11/09 20:54)
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