對於R上可導的任意函數f(x),若滿足(x-1)f′(x)≥0,則必有() 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)

對於R上可導的任意函數f(x),若滿足(x-1)f′(x)≥0,則必有() 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)

依題意,當x≥1時,f′(x)≥0,函數f(x)在(1,+∞)上是增函數;當x<1時,f′(x)≤0,f(x)在(-∞,1)上是减函數,故當x=1時f(x)取得極小值也為最小值,即有f(0)≥f(1),f(2)≥f(1),∴f(0)+f(2)≥2f(1).故選C.