作业帮设函数f(x)=[1/ln(x+1)]-1/x,(x＞-1,x≠0).(1)当x＞0时,求证:f(x)＜1/2.(2)求证:函数f(x)在定义域内为减函数.
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![设函数f(x)=[1/ln(x+1)]-1/x,(x＞-1,x≠0).(1)当x＞0时,求证:f(x)＜1/2.(2)求证:函数f(x)在定义域内为减函数.](/uploads/image/z/6783545-65-5.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3D%5B1%2Fln%28x%2B1%29%5D-1%2Fx%2C%28x%EF%BC%9E-1%2Cx%E2%89%A00%29.%281%29%E5%BD%93x%EF%BC%9E0%E6%97%B6%2C%E6%B1%82%E8%AF%81%3Af%28x%29%EF%BC%9C1%2F2.%282%29%E6%B1%82%E8%AF%81%3A%E5%87%BD%E6%95%B0f%28x%29%E5%9C%A8%E5%AE%9A%E4%B9%89%E5%9F%9F%E5%86%85%E4%B8%BA%E5%87%8F%E5%87%BD%E6%95%B0.)
设函数f(x)=[1/ln(x+1)]-1/x,(x＞-1,x≠0).(1)当x＞0时,求证:f(x)＜1/2.(2)求证:函数f(x)在定义域内为减函数.
设函数f(x)=[1/ln(x+1)]-1/x,(x＞-1,x≠0).(1)当x＞0时,求证:f(x)＜1/2.(2)求证:函数f(x)在定义域内为减函数.
设函数f(x)=[1/ln(x+1)]-1/x,(x＞-1,x≠0).(1)当x＞0时,求证:f(x)＜1/2.(2)求证:函数f(x)在定义域内为减函数.
f（x）的导数=-1/{(x+1)[ln(x+1)]^2}+1/x^2
又x^2>(x+1)[ln(x+1)]^2(令g(x)=x^2-(x+1)[ln(x+1)]^2再求导可得)
故f(x)的导数在定义域内0时无解,所以当x>0时,f（x）
证明函数导数小于0