f(x)=-x3-6x2-9x-2.
f'(x)=-3x2-12x-9=0 at a turning point.
Divide through by -3: x2+4x+3=0=(x+3)(x+1). So there are turning points at x=-1, -3.
f(-1)=1-6+9-2=2; f(-3)=27-54+27-2=-2. Turning points at (-1,2) and (-3,-2).
f''(x)=-6x-12. f''(-1)<0 (maximum); f''(-3)>0 (minimum).
Max at (-1,2), min at (-3,-2). Therefore f(x) is decreasing (-∞,-3], increasing [-3,-1], decreasing [-1,∞).