∴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.