The tangent slope of curve y=f(x) at points (a+ 1, f(a+ 1)) is:

f'(a+ 1)=3(a+ 1)^2-3a(a+ 1)= 12

a= 1 1

(2)

1 & lt； A<2, then 3/2

f'(x)=3x(x-a)

Because 1

So x=a is not in the interval [- 1, 1].

F(x) reaches the maximum when x=0.

Therefore, the maximum value of f(x) in the interval [- 1, 1] is f(0)=b= 1.

f(x)=x^3-(3/2)ax^2+ 1

f(- 1)=-(3/2)a

f( 1)=2-(3/2)a

So f (- 1) < F( 1), that is, f (- 1) is the minimum value.

f(- 1)=-(3/2)a=-2、a=4/3 .

The analytical formula is: f (x) = x 3-2x 2+ 1.