如题,已知f(x)=(x+1)lnx-x+1,证明(x-1)f(x)大于等于0 ,
问题描述:
如题,已知f(x)=(x+1)lnx-x+1,证明(x-1)f(x)大于等于0 ,
答
令g(x)=(x-1)f(x)=(x²-1)lnx-(x-1)²定义域x>0,且g(1)=0g'(x)=(x²-1)/x+2xlnx-2(x-1)g'(1)=0,x=1为g(x)的唯一极值点g'(e)=e-1/e+2e-2(e-1)=e-1/e+2>0g'(1/e)=1/e-e-2/e+2(1/e-1)=1/e-e-2=0...