Te main problem is to find beta in this equation fu

Question

The main problem is to find β in this equation:

F(u) = ωu(u-β)(1-u)

If is it β ≤ -1 ????

Or

-1 ≤ β ≤ 0

Or

β > 0 ???

The solution step:

1. F(u)  = ωu(u- β) (1-u)

2. F'(u)  = ω(u-β)(1-u) + ωu(1-u) - ωu (u-β)

             = ωu - ωu² - ωβ + ωβu + ωu(1-u) - ωu(u-β)

             = -3ωu² + 2ωu + 2ωβu - ωβ.

3. Now we have find u_max (Hint- u_max: F'(u)= 0.)  

4. we have to find max F = F(u_max) from this we can found β = ???