2 A bird flies from a tree. At time \(t\) seconds, the bird's height, \(y\) metres, above the horizontal ground is given by
$$y = \frac { 1 } { 8 } t ^ { 4 } - t ^ { 2 } + 5 , \quad 0 \leqslant t \leqslant 4$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} t }\).
- Find the rate of change of height of the bird in metres per second when \(t = 1\).
- Determine, with a reason, whether the bird's height above the horizontal ground is increasing or decreasing when \(t = 1\).
- Find the value of \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} t ^ { 2 } }\) when \(t = 2\).
- Given that \(y\) has a stationary value when \(t = 2\), state whether this is a maximum value or a minimum value.