作业帮设函数f(x)=x-(x+1)ln(x+1)(x>-1)(1)求f(x)的单调区间(2)证明:当n>m>0时,(1+n)^m2012,且X1,X2,X3,……,Xn属于R+,X1+X2+X3+……+Xn=1时,①X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)>=1/(1+n)②[X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)]^(
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![设函数f(x)=x-(x+1)ln(x+1)(x>-1)(1)求f(x)的单调区间(2)证明:当n>m>0时,(1+n)^m2012,且X1,X2,X3,……,Xn属于R+,X1+X2+X3+……+Xn=1时,①X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)>=1/(1+n)②[X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)]^(](/uploads/image/z/6747704-8-4.jpg?t=%E8%AE%BE%E5%87%BD%E6%95%B0f%28x%29%3Dx-%28x%2B1%29ln%28x%2B1%29%28x%3E-1%29%281%29%E6%B1%82f%28x%29%E7%9A%84%E5%8D%95%E8%B0%83%E5%8C%BA%E9%97%B4%282%29%E8%AF%81%E6%98%8E%3A%E5%BD%93n%3Em%3E0%E6%97%B6%2C%281%2Bn%29%5Em2012%2C%E4%B8%94X1%2CX2%2CX3%2C%E2%80%A6%E2%80%A6%2CXn%E5%B1%9E%E4%BA%8ER%2B%2CX1%2BX2%2BX3%2B%E2%80%A6%E2%80%A6%2BXn%3D1%E6%97%B6%2C%E2%91%A0X1%5E2%2F%281%2BX1%29%2BX2%5E2%2F%281%2BX2%29%2B%E2%80%A6%E2%80%A6%2BXn%5E2%2F%281%2BXn%29%3E%3D1%2F%281%2Bn%29%E2%91%A1%5BX1%5E2%2F%281%2BX1%29%2BX2%5E2%2F%281%2BX2%29%2B%E2%80%A6%E2%80%A6%2BXn%5E2%2F%281%2BXn%29%5D%5E%28)
设函数f(x)=x-(x+1)ln(x+1)(x>-1)(1)求f(x)的单调区间(2)证明:当n>m>0时,(1+n)^m2012,且X1,X2,X3,……,Xn属于R+,X1+X2+X3+……+Xn=1时,①X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)>=1/(1+n)②[X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)]^(
设函数f(x)=x-(x+1)ln(x+1)(x>-1)
(1)求f(x)的单调区间
(2)证明:当n>m>0时,(1+n)^m2012,且X1,X2,X3,……,Xn属于R+,X1+X2+X3+……+Xn=1时,
①X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)>=1/(1+n)
②[X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)]^(1/n)>(1/2013)^(1/2012)
设函数f(x)=x-(x+1)ln(x+1)(x>-1)(1)求f(x)的单调区间(2)证明:当n>m>0时,(1+n)^m2012,且X1,X2,X3,……,Xn属于R+,X1+X2+X3+……+Xn=1时,①X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)>=1/(1+n)②[X1^2/(1+X1)+X2^2/(1+X2)+……+Xn^2/(1+Xn)]^(
1）f'(x)=-ln(x+1) 所以f 在(-1,0]上严格单调递增,[0,正无穷）上严格单调递减
从而f的最大值为0且对任意x>0,f(x)