Let the minimum value of F (x) = ax ^ 3 + BX ^ 2 + CX be - 8, and the image of its derivative function y = f '(x) passes through points (- 2,0) and (2 / / 3,0), as shown in the figure (1) Finding the analytic expression of F (x) (2) If f (x) ≥ m ^ 2-14m holds for X ∈ [- 3,3], the value range of real number m is obtained (the picture shows: the opening of the image is downward, the intersection of the image and the X axis is - 2,2 / 3, and the intersection of the image and the Y axis is above.)

Let the minimum value of F (x) = ax ^ 3 + BX ^ 2 + CX be - 8, and the image of its derivative function y = f '(x) passes through points (- 2,0) and (2 / / 3,0), as shown in the figure (1) Finding the analytic expression of F (x) (2) If f (x) ≥ m ^ 2-14m holds for X ∈ [- 3,3], the value range of real number m is obtained (the picture shows: the opening of the image is downward, the intersection of the image and the X axis is - 2,2 / 3, and the intersection of the image and the Y axis is above.)

F '(x) = 3ax ^ 2 + 2bx + C, from the condition 3A (- 2) ^ 2 + 2B (- 2) + C = 0, 3A (2 / 3) ^ 2 + 2B (2 / 3) + C = 0, in addition, the derivative function is 0 on (negative infinity, - 2) and (2 / 3, + infinity), so f (x) decreases first and then increases and decreases, and - 2 is the minimum point, so a (- 2) ^ 3 + B (- 2) ^ 2 + C (- 2) = - 8