1，f' (x) = 3x 2+2x - 1 = 3。 If f'(x)=0, then x1=-1x2 =1/3. Because the opening is upward, it goes from negative infinity to -65438+.

2, f'(x)=3+2x makes f'(x)=0 and x=-3/2, so it decreases from negative infinity to -3/2 and increases from -3/2 to positive infinity.

3. If f'(x)=4x-3 makes f'(x)=0 and x=3/4, then it decreases from negative infinity to 3/4 and increases from 3/4 to positive infinity.

4.F' (x) = 6x2 No matter what the value of x is, f' (x) > =0, so it is a monotonically increasing function.

5.f'(x)= 1-sinx f'(x)>0, so this function is monotonically increasing.

6, f'(x)=-2, so this function is monotonically decreasing.