设f(x)在[a,b]上连续可导,且f(a)=f(b)=0.证明: |f(x)|≤|f’(x)|dx(a<x<b).

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问题 设f(x)在[a,b]上连续可导,且f(a)=f(b)=0.证明:
|f(x)|≤|f’(x)|dx(a<x<b).

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答案因为[*]且f(a)=f(b)=0,所以 [*]两式相加得|f(x)|≤[*]|f’(x)|dx.

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