F (x) = ax ^ 3 + BX + C (a is not equal to 0) is an odd function, the tangent of its image at (1, f (1)) is parallel to the straight line 6x + y + 7 = 0, and the minimum value of F '(x) is - 12 1. Find the value of a, B, C 2. Find the monotone increasing interval of function f (x), and find the maximum and minimum of function f (x) on [- 1,3]

F (x) = ax ^ 3 + BX + C (a is not equal to 0) is an odd function, the tangent of its image at (1, f (1)) is parallel to the straight line 6x + y + 7 = 0, and the minimum value of F '(x) is - 12 1. Find the value of a, B, C 2. Find the monotone increasing interval of function f (x), and find the maximum and minimum of function f (x) on [- 1,3]

1. Because f is an odd function, f (0) = 0 is brought in to get C = 0, so f (x) = ax ^ 3 + BX is derived from F. the slope of F '= 3ax ^ 2 + B at x = 1 is: F' (1) = 3A + B, because the tangent at point (1, f (1)) is parallel to 6x + y + 7 = 0, then 3A + B = - 6, because f 'has the minimum value, so the opening of quadratic function f' is upward, a > 0 and the minimum