6 The parametric equations of a curve are
$$x = 2 t + \ln t , \quad y = t + \frac { 4 } { t }$$
where \(t\) takes all positive values.
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { t ^ { 2 } - 4 } { t ( 2 t + 1 ) }\).
- Find the equation of the tangent to the curve at the point where \(t = 1\).
- The curve has one stationary point. Find the \(y\)-coordinate of this point, and determine whether this point is a maximum or a minimum.