For any differentiable function f (x) on R, if (x-1) f ′ (x) ≥ 0, then () A. f（0）+f（2）＜2f（1）B. f（0）+f（2）≤2f（1）C. f（0）+f（2）≥2f（1）D. f（0）+f（2）＞2f（1）

According to the meaning of the problem, when x ≥ 1, f '(x) ≥ 0, the function f (x) is an increasing function on (1, + ∞); when x < 1, f' (x) ≤ 0, f (x) is a decreasing function on (- ∞, 1), so when x = 1, the minimum value of F (x) is also the minimum value, that is, f (0) ≥ f (1), f (2) ≥ f (1), f (0) + F (2) ≥ 2F (1)

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