微分中值定理与导数的应用中的一道题设f(x)在[0,1]上连续,在(0,1)内可导,且f(0)=0,f(1)=1,试证明对任意给定的正数a及b,在(0,1)内存在不相等的x1,x2,使a/f‘(x1)+b/f’(x2)=a+b
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![微分中值定理与导数的应用中的一道题设f(x)在[0,1]上连续,在(0,1)内可导,且f(0)=0,f(1)=1,试证明对任意给定的正数a及b,在(0,1)内存在不相等的x1,x2,使a/f‘(x1)+b/f’(x2)=a+b](/uploads/image/z/4056854-14-4.jpg?t=%E5%BE%AE%E5%88%86%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E4%B8%8E%E5%AF%BC%E6%95%B0%E7%9A%84%E5%BA%94%E7%94%A8%E4%B8%AD%E7%9A%84%E4%B8%80%E9%81%93%E9%A2%98%E8%AE%BEf%EF%BC%88x%EF%BC%89%E5%9C%A8%5B0%2C1%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%EF%BC%880%2C1%EF%BC%89%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E4%B8%94f%EF%BC%880%EF%BC%89%3D0%2Cf%EF%BC%881%EF%BC%89%3D1%2C%E8%AF%95%E8%AF%81%E6%98%8E%E5%AF%B9%E4%BB%BB%E6%84%8F%E7%BB%99%E5%AE%9A%E7%9A%84%E6%AD%A3%E6%95%B0a%E5%8F%8Ab%2C%E5%9C%A8%EF%BC%880%2C1%EF%BC%89%E5%86%85%E5%AD%98%E5%9C%A8%E4%B8%8D%E7%9B%B8%E7%AD%89%E7%9A%84x1%2Cx2%2C%E4%BD%BFa%2Ff%E2%80%98%EF%BC%88x1%EF%BC%89%2Bb%2Ff%E2%80%99%EF%BC%88x2%EF%BC%89%3Da%2Bb)
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