Question

f (x )=ax +(a -1)lnx +x /1-2的单调性

Answer 1

问：f (x )=ax +(a -1)lnx +x /1-2的单调性

答：f'(x)=x-a+(a-1)/x=[x-(a-1)](x-1)/x|) 当10,f(x)单调递增x∈(a-1,1),f(x)<0,f(x)单调递减x∈(1,+o),f'(x)>0,f(x)单调递增I)当a=2,f(x)=(x-1)2/x>=0, 且f(x)不恒为0,f(2,时x∈(0,1),f'(x)>0,f(x)单调递增x∈(1 ,a-1),f'(x)<0,f(x)单调递减X∈(a-1,+o),f'(x)>O,f(x)单调递增