The function f (x) = x ^ 3 + ax ^ 2 + BX (a, B are constants) defined on R obtains the extremum at x = - 1. The tangent of the image of F (x) at point P (1, t) is parallel to The function f (x) = x ^ 3 + ax ^ 2 + BX (a, B are constants) defined on R obtains the extremum at x = - 1, and the tangent of the image of F (x) at point P (1, t) is parallel to the straight line y = 8x. (1) find the analytic expression of function f (x); (2) find the maximum and minimum of function f (x)

The function f (x) = x ^ 3 + ax ^ 2 + BX (a, B are constants) defined on R obtains the extremum at x = - 1. The tangent of the image of F (x) at point P (1, t) is parallel to The function f (x) = x ^ 3 + ax ^ 2 + BX (a, B are constants) defined on R obtains the extremum at x = - 1, and the tangent of the image of F (x) at point P (1, t) is parallel to the straight line y = 8x. (1) find the analytic expression of function f (x); (2) find the maximum and minimum of function f (x)

(1) F '(x) = 3x ^ 2 + 2aX + B, from the known f' (- 1) = 3-2a + B = 0, f '(1) = 3 + 2A + B = 8, the solution is a = 2, B = 1, f (x) = x ^ 3 + 2X ^ 2 + X
(2) If f '(x) > 0, X-1 / 3; f' (x)