2. The derivative of the function at (1, f( 1)) is the tangent slope of this point, so k=0.

3. So f( 1) is the intercept of this point on the Y axis, so: f( 1)=2a+b=3, b=3-2a.

4.In (1, positive infinity) f (x)-x >; 0, f(x)-x=(a- 1)x+a/x+b, and the scaling f(x)-x is greater than or equal to "2 times under the root of a(a- 1)+b" according to the formula.

Ensure that f (x)-x >; 0, then the quadratic root of "a(a- 1)+b" is greater than 0. Get: a

So choose B.