The derivative problem is solved by F (x) = x ^ 3 + 3ax-1, let a = - m ^ 2, when the real number m changes in what range, y = f (x) and y = 3 have only one common point? The first floor is not right at all.

The derivative problem is solved by F (x) = x ^ 3 + 3ax-1, let a = - m ^ 2, when the real number m changes in what range, y = f (x) and y = 3 have only one common point? The first floor is not right at all.

f(x)=x^3-3m^2x-1
f'(x)=3x^2-6m^2=0
x=±√2m
Then x √ 2 | m |, f '(x) > 0, increasing
-√2|m|-√2
m> = 0, √ 2m ^ 3 √ 2, not true
m>=0,√2m^3