10 The function f is defined by \(\mathrm { f } ( x ) = ( 4 x + 2 ) ^ { - 2 }\) for \(x > - \frac { 1 } { 2 }\).
- Find \(\int _ { 1 } ^ { \infty } \mathrm { f } ( x ) \mathrm { d } x\).
A point is moving along the curve \(y = \mathrm { f } ( x )\) in such a way that, as it passes through the 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. - Find the coordinates of \(A\).