∴f'(x)= 1+f(x)/x，

f''(x)=[xf'(x)-f(x)]/x^2= 1/x，

∴f'(x)=lnx+b，

f( 1)= 1，f'( 1)=2=b，

f'(x)=lnx+2，

f(x)=xlnx+x+c，

∴ 1= 1+c，

∴c=0，

∴f(x)=xlnx+x.

① ② ③ Correct,

Let g (x) = f (x)-x 2, g' (x) = lnx+2-2x, g'' (x) = 1/x-2,

0<x & ltG'' (x) at 1/2 >: 0, g'(x) is increasing function, others, g'(x) is a decreasing function,

∴g'(x)<； =g'( 1/2)= 1-ln2，g'( 1)=0，

0<x & ltG' (x) at 1 >: 0, g(x) is increasing function; Otherwise, g(x) is a decreasing function,

∴g(x)<； =g( 1)=0，

4 established.

Choose D.