∵f(x)=x3-3x2-9x
∴f'(x)=3(x^2+2x-3)
令f'(x)=3(x^2+2x-3)=0
则f'(x)的零点为 x=-3 x=1
所以f(x)的单调增区间是 x=1
f(x)的单调减区间：-3