Given the function y = f (x) = x2 + 3x + 2aX, X ∈ [2, + ∞); (1) when a = 12, find the minimum value of function f (x); (2) if f (x) > 0 holds for any x ∈ [2, + ∞), find the value range of real number a

Given the function y = f (x) = x2 + 3x + 2aX, X ∈ [2, + ∞); (1) when a = 12, find the minimum value of function f (x); (2) if f (x) > 0 holds for any x ∈ [2, + ∞), find the value range of real number a

(1) When a = 12, f (x) is (f (x) = x2 + 3x + 3x + 1x + 3, and f ′ (x) = 1 {1x2 = x2 \\\ = 12, f (x) = x (x) is (f (x) = x2 + 3x + 3x + 3 + 3 + 3, f (x) = x (x) is the increasing function of F (x) = x (x) = x (x) = x (2 + 2 + 12 + 12 + 3 + 3 + 3 + 3 = 112, f (2) is the result of F (x), y has x + 3x + 3 x + 2x + 2aX x + 2aX x + 2aX x x 2x \\\\\\\\\\\)=- So the value range of real number a; (- 5, + ∞)