It is known that f (x) = ax ^ 3 + BX ^ 2 + CX (a is not equal to 0) obtains the extremum when x = ± 1, and f (1) = - 1,1) tries to find the value of constant ABC It is known that f (x) = ax ^ 3 + BX ^ 2 + CX (a is not equal to 0) obtains the extremum when x = ± 1, and f (1) = - 1,1) tries to find the value of constant ABC; 2) tries to judge whether the function obtains the minimum or maximum when x = ± 1, and explains the reason

It is known that f (x) = ax ^ 3 + BX ^ 2 + CX (a is not equal to 0) obtains the extremum when x = ± 1, and f (1) = - 1,1) tries to find the value of constant ABC It is known that f (x) = ax ^ 3 + BX ^ 2 + CX (a is not equal to 0) obtains the extremum when x = ± 1, and f (1) = - 1,1) tries to find the value of constant ABC; 2) tries to judge whether the function obtains the minimum or maximum when x = ± 1, and explains the reason

f'(x)=3ax^2+2bx+c
f(1)=-1
∴-a+b-c=1
The maximum value is obtained when x = ± 1
∴f'(-1)=3a-2b+c=0
f'(1)=3a+2b+c=0
∴b=0
3a+c=0
a+c=-1
Solution
a=1/2
c=-3/2
∴f'(x)=3/2x^2-3/2
Let f '(x) = 3 / 2x ^ 2-3 / 2 > = 0
x^2>=1
x=1
The increasing intervals of F (x) are (- ∞, - 1] and [1, + ∞)
The minus interval is [- 1,1]
X = - 1, f (x) has a maximum
X = 1, f (x) has a minimum