analyse

Let g (x) = f (x)/x n.

Then g' (x) = [xf' (x)-nf (x)]/x (n+1)

According to the meaning of the question, within (0, +∞)

g'(x)>0

∴g(x) increases monotonously.

∴g(2)>g( 1)

∴f(2)/f( 1)>2^n

∴2^n≥4

∴n≥2

Let h (x) = f (x)/x (n+ 1)

Then h' (x) = [xf' (x)-(n+1) f (x)]/x (n+2).

According to the meaning of the question, within (0, +∞)

h'(x)h( 1)

∴f(2)/f( 1)