IIT JEE 2009 P2 Q26

For th efunction

f(x) = x cos 1/x , x>=1

A) for atleast one x in the interval [1,∞), f(x+2)-f(x)<2
B) lim x->∞ f'(x) = 1
C) for all x in the interval [1,∞) , f(x+2)-f(x) >2
D) f'(x) is strictly decreasing in the interval [1,∞)

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