$ f(x) = \frac {x}{x^2 + 9} + \frac {1}{x^2 - 6x + 21} + \cos {2 \pi x}\ (x > 0).$ $ \leq \frac {x}{(x - 3)^2 + 6x} + \frac {1}{(x - 3)^2 + 12} + \cos 2\pi x\leq \boxed{\frac {5}{4}}$ when $ x = 3.$ You can also use AM-GM.