The function f (x) = 12x2 + alnx (a ∈ R) is known. (I) if the tangent equation of the image of F (x) at x = 2 is y = x + B, find the value of a and B; (II) if f (x) is an increasing function at (1, + ∞), find the value range of A

The function f (x) = 12x2 + alnx (a ∈ R) is known. (I) if the tangent equation of the image of F (x) at x = 2 is y = x + B, find the value of a and B; (II) if f (x) is an increasing function at (1, + ∞), find the value range of A

(I) given the function f (x) = 12x2 + alnx, then the tangent equation of the image of derivative f ′ (x) = x + ax function f (x) at x = 2 is y = x + B. It can be known that f ′ (2) = 2 + A2 = 1, f (2) = 2 + aln2 = 2 + B, the solution is a = - 2, B = - 2ln2 (II) if the function f (x) is an increasing function on (1, + ∞), then f ′ (x) = x + ax ≥ 0 is constant on (1, + ∞), the separation of variables is a ≥ - X2, and (- x2) is on X If ∈ (1, + ∞) is always less than - 1, then a ≥ - 1 is obtained, so the value range of a is a ≥ - 1