求解两道高数中值定理题第一题:设函数f(x)在区间[a,b]上连续(a>0),在(a,b)上可微,且f'(x)≠0.证明存在ξ,η∈(a,b),使得f'(ξ)=[(a+b)/2η]f'(η).第二题:设函数f(x)在区间(0,1)上连续,在(0,1)内可导,试证
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![求解两道高数中值定理题第一题:设函数f(x)在区间[a,b]上连续(a>0),在(a,b)上可微,且f'(x)≠0.证明存在ξ,η∈(a,b),使得f'(ξ)=[(a+b)/2η]f'(η).第二题:设函数f(x)在区间(0,1)上连续,在(0,1)内可导,试证](/uploads/image/z/5568275-11-5.jpg?t=%E6%B1%82%E8%A7%A3%E4%B8%A4%E9%81%93%E9%AB%98%E6%95%B0%E4%B8%AD%E5%80%BC%E5%AE%9A%E7%90%86%E9%A2%98%E7%AC%AC%E4%B8%80%E9%A2%98%EF%BC%9A%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%5Ba%2Cb%5D%E4%B8%8A%E8%BF%9E%E7%BB%AD%28a%3E0%29%2C%E5%9C%A8%28a%2Cb%29%E4%B8%8A%E5%8F%AF%E5%BE%AE%2C%E4%B8%94f%27%28x%29%E2%89%A00.%E8%AF%81%E6%98%8E%E5%AD%98%E5%9C%A8%CE%BE%2C%CE%B7%E2%88%88%28a%2Cb%29%2C%E4%BD%BF%E5%BE%97f%27%28%CE%BE%29%3D%5B%28a%2Bb%29%2F2%CE%B7%5Df%27%28%CE%B7%29.%E7%AC%AC%E4%BA%8C%E9%A2%98%EF%BC%9A%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E5%8C%BA%E9%97%B4%280%2C1%29%E4%B8%8A%E8%BF%9E%E7%BB%AD%2C%E5%9C%A8%280%2C1%29%E5%86%85%E5%8F%AF%E5%AF%BC%2C%E8%AF%95%E8%AF%81)
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