This process is a bit of a jump,

f'(x)=-(x- 1/2)？ + 1/4-2a

It is a quadratic function, the image opening is downward, and the symmetry axis x = 1/2.

The maximum value of f'(x) is f'(2/3).

In order to satisfy the meaning of the question,

That is to say, f'(x) can take a positive number.

Only the maximum value of f'(x) is required to be > 0.

Namely f' (2/3) >: 0