The monotonic increasing interval of the function f (x) = ax 3+bx 2+CX (a ≠ 0) defined on R is (-1. 1). If equation 3a (f (x)) 2+2bf (x)+c = 0 has exactly six different real roots.

f'(x)=3ax^2+2bx+c

f'(- 1)=f'( 1)=0

3a-2b+c=3a+2b+c=0 b=0，c=-3a

f( 1)= a-2 b+ c =-2a & gt； 1

a & lt- 1/2

It is easy to verify that f (x) = ax 3-3ax meets the meaning of the question.

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