(a)[4]
Evaluate $\int_{1}^{\infty} f(x)\,dx$.
(b)[6]
A point moves along the curve $y = f(x)$ so that, as it passes through point $A$, its $y$-coordinate is decreasing at the rate of $k$ units per second and its $x$-coordinate is increasing at the rate of $k$ units per second. Determine the coordinates of $A$.