证明函数恒等式设f(x)在〔0,+∞)上连续,在(0,+∞)内可导且满足f(0)=0,f(x)≥0,f(x )≥f‘(x)(x>0),求证f(x)≡0
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![证明函数恒等式设f(x)在〔0,+∞)上连续,在(0,+∞)内可导且满足f(0)=0,f(x)≥0,f(x )≥f‘(x)(x>0),求证f(x)≡0](/uploads/image/z/12076046-62-6.jpg?t=%E8%AF%81%E6%98%8E%E5%87%BD%E6%95%B0%E6%81%92%E7%AD%89%E5%BC%8F%E8%AE%BEf%EF%BC%88x%EF%BC%89%E5%9C%A8%E3%80%940%2C%EF%BC%8B%E2%88%9E%EF%BC%89%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%EF%BC%880%2C%EF%BC%8B%E2%88%9E%EF%BC%89%E5%86%85%E5%8F%AF%E5%AF%BC%E4%B8%94%E6%BB%A1%E8%B6%B3f%EF%BC%880%EF%BC%89%3D0%2Cf%EF%BC%88x%EF%BC%89%E2%89%A50%2Cf%EF%BC%88x+%EF%BC%89%E2%89%A5f%E2%80%98%EF%BC%88x%EF%BC%89%EF%BC%88x%EF%BC%9E0%EF%BC%89%2C%E6%B1%82%E8%AF%81f%EF%BC%88x%EF%BC%89%E2%89%A10)
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证明函数恒等式设f(x)在〔0,+∞)上连续,在(0,+∞)内可导且满足f(0)=0,f(x)≥0,f(x )≥f‘(x)(x>0),求证f(x)≡0
证明函数恒等式
设f(x)在〔0,+∞)上连续,在(0,+∞)内可导且满足f(0)=0,f(x)≥0,f(x )≥f‘(x)(x>0),求证f(x)≡0
证明函数恒等式设f(x)在〔0,+∞)上连续,在(0,+∞)内可导且满足f(0)=0,f(x)≥0,f(x )≥f‘(x)(x>0),求证f(x)≡0
由f(x)>=f'(x)得,e^(-x)f(x)-f'(x)e^(-x)=[e^(-x)f(x)]'>=0,所以e^(-x)f(x)