Let the function f (x) = - 1,3x3 + x2 + (M2-1) x belong to R, and find the monotone interval and extremum of the function

Let the function f (x) = - 1,3x3 + x2 + (M2-1) x belong to R, and find the monotone interval and extremum of the function

f'(x)=-x²+2x+m²-1=-(x-1)²+m²=-(x-1+m)(x-1-m)
The extreme point is x = 1-m, 1 + M
Discussion M:
1) If M = 0, then f '(x) = - (x-1) & # 178; > = 0, the function is monotonically decreasing on R and has no extremum;
2) If M > 0, the monotone increasing interval is: (1-m, 1 + m),
The monotone decreasing interval is: (- ∞, 1-m) U (1 + m, + ∞)
The minimum is f (1-m) = - (1-m) &# 178; (1 + 2m) / 3
The maximum is f (1 + m) = - (1 + m) &# 178; (1-2m) / 3
3) If M