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For the function $$f(x) = x \cos \frac{1}{x}, x \geq 1$$,
for at least one x x in the interval $$[1, \infty), f(x + 2) - f(x) < 2$$
$$\lim_{x \rightarrow \infty}f'(x) = 1$$
for all x in the interval $$[1, \infty), f(x + 2) - f(x) > 2$$
f'(x) is strictly decreasing in the interval $$[1, \infty)$$
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