For the function
$$f(x) = x \cos \frac{1}{x}, x \geq 1$$,

A

for at least one x x in the interval $$[1, \infty), f(x + 2) - f(x) < 2$$

B

$$\lim_{x \rightarrow \infty}f'(x) = 1$$

C

for all x in the interval $$[1, \infty), f(x + 2) - f(x) > 2$$

D

f'(x) is strictly decreasing in the interval $$[1, \infty)$$