f'(x)=3x^2+2x+a

=3x^2+2x- 1

=(x+ 1)(3x- 1)

x 1=- 1 x2= 1/3

(-∞,-1)( 1/3,+∞) is an increasing interval.

(-1, 1/3) is the subtraction interval.

2) let g (x) = x 3+x 2+ax+b-ax = x 3+x 2+b.

g'(x)=3x^2+2x

=x(3x+2)

x 1=0 x2=-2/3

(-∞, -2/3)(0,+∞) is an increasing interval.

(-2/3,0) is the subtraction interval.

So a g (-2/3) * g (0) < 0.

b∈(-4/27，0)