Given that the image of the function f (x) = AX3 + bx2 + CX + D (a ≠ 0) passes through the origin, f ′ (1) = 0, if f (x) reaches the maximum at x = - 1, 2. (1) find the analytic expression of the function y = f (x); (2) if f (x) ≥ f ′ (x) + 6x + m for any x ∈ [- 2,4], find the maximum of M

Given that the image of the function f (x) = AX3 + bx2 + CX + D (a ≠ 0) passes through the origin, f ′ (1) = 0, if f (x) reaches the maximum at x = - 1, 2. (1) find the analytic expression of the function y = f (x); (2) if f (x) ≥ f ′ (x) + 6x + m for any x ∈ [- 2,4], find the maximum of M

(1) ∵ f ′ (x) = 3ax2 + 2bx + C (a ≠ 0), when∵ x = - 1, there is a maximum of 2, ∵ f ′ (- 1) = 3a-2b + C = 0 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ① and f (0) = D = 0 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ② f ′ (1) = 3A + 2B + C = 0 & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; ③ f (- 1)