\(f(x)\) is defined as \(f(x)=2k+14x-x^{2}\) , \(x\in\mathbb{R}\), \(x>0\).

\(k = \frac{\ln((e^{2{\ln}e + \ln(-e^{2}) + \ln(-e^{3})})(-e^{-1})) - \ln{e^{\imath\pi-5}}}{(2\sec^{2}x - \cos^{3}\tan^{3}\sec^{2}\cot^{2}\sin x - 2\tan^{2}x + \sin^{2}x)^{-1}}\)

Find the maximum value of \(f(x)\).

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