Question #41377

The problem requires finding the global maximum of a function with a periodic inverse trigonometric term and a logarithmic singularity.

The primary trap is the 'cross-multiplication trap' (Concept 62): when solving $f'(x) > 0$ on $(0, \pi/2)$, students encounter $\frac{x-\sqrt{3}+1}{x-\sqrt{3}} > 0$.

If they cross-multiply by the variable denominator $x-\sqrt{3}$ without noting it is strictly negative on this interval, they will incorrectly classify the critical point $x = \sqrt{3}-1$ as a local minimum.

Consequently, they will hunt for the maximum at the endpoints or the non-differentiable cusp at $x=\pi/2$ (Concept 209), leading to incorrect options like $\ln\sqrt{3}$.

The problem forces rigorous sign analysis around asymptotes and cusps.