It is known that the derivative of quadratic function f (x) = AX2 + BX + C is f '(x), f' (0) & gt; 0. For any real number x, if f (x) ≥ 0, then the minimum value of F (1) f '(0) is () A. 2B. 52C. 3D. 32

∵ f (x) ≥ 0, we know that a & gt; 0 △ = B2 − 4ac ≤ 0, ∵ C ≥ b24a. Also, f ′ (x) = 2aX + B, ∵ f ′ (0) = B & gt; 0, f (1) = a + B + C. ∵ f (1) f ′ (0) = 1 + A + CB ≥ 1 + A + b24ab = 1 + 4a2 + b24ab ≥ 1 + 24a2b24ab = 2. If and only if 4a2 = B2, "=" is true. Therefore, select a

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