I hope the teacher can explain It is known that the function f (x) whose domain is [0,1] satisfies the following three conditions at the same time 1. For any x ∈ [0,1], there is always f (x) ≥ 0 2、f（1）=1 3. When x ≥ 0, y ≥ 0, and X + y ″ 1, f (x + y) ≥ f (x) + F (y) (1) Try to find the value of F (0) (2) . find the maximum of F (x) (3) It is proved that when x belongs to [1 / 4,1], there is always 2x ≥ f (x)

I hope the teacher can explain It is known that the function f (x) whose domain is [0,1] satisfies the following three conditions at the same time 1. For any x ∈ [0,1], there is always f (x) ≥ 0 2、f（1）=1 3. When x ≥ 0, y ≥ 0, and X + y ″ 1, f (x + y) ≥ f (x) + F (y) (1) Try to find the value of F (0) (2) . find the maximum of F (x) (3) It is proved that when x belongs to [1 / 4,1], there is always 2x ≥ f (x)

(1)
f(x+y)≥f(x)+f(y).
f(1)=f(1+0)≥f(0)+f(1)
∴f(0）≤0
It is also true that f (x) ≥ 0
∴f(0)=0
(2)
Take 0 ≤ M