It is known that the derivative f '(x) ≤ f (x) B of quadratic function f (x) = AX2 + BX + C belongs to R. it is proved that f (x) is less than or equal to (x + C) ^ 2 when x ≥ 0

It is known that the derivative f '(x) ≤ f (x) B of quadratic function f (x) = AX2 + BX + C belongs to R. it is proved that f (x) is less than or equal to (x + C) ^ 2 when x ≥ 0

The derivation is: F (x) '= 2x + B
Because all x belongs to all x belongs to R, all x belongs to all x belongs to all x belongs to R, because of all x belongs to all x belongs to R: 2x + B ≤ x ^ 2 ≤ x ^ 2 + x ^ 2 + BX + C constant, that is: x ^ 2 + (b-2) x + (C-B) ≥ 0, this inequality is a constant, this inequality is a constant, which is equivalent to the discriminant △ = (b-2-2) ^ 2-2-2 ^ 2-2 ^ 2 (b-2-2) x + (c-2-2-2 (B-2 / 2 / 4) x + (C ^ 2-2-1-1 ≥ 0, the mean inequality is: C ≥ 2 {[(b ^ 2 ^ 2 ^ 2 / 2 / 2 / 4) + (1) + 1] = [1] = [b, by the mean inequality is: C ≥ 0: C ≥ 2 [(B \(B (b ^ 2 ^ 2 ^ 2 ^ 2> 0, So when x ≥ 0, there is always (x + C) ^ 2-F (x) = (2C-B) x + (C ^ 2-1) ≥ 0, that is, the life problem f (x) ≤ (x + C) ^ 2 holds