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.