Given:

f(x) = x³+6x²+9x+3.

f’(x) = 3x²+12x+9 = 0

f’(x) = 3(x²+4x+3) =0

f’(x) = 3(x+1)(x+3) = 0

x = -1 or x =-3

for x>-1 f(x) is increasing

for x<-3 f(x) is increasing

But for -1<x<-3 it is decreasing.