3 The depth of water, \(y\) metres, in a tank after time \(t\) hours is given by
$$y = \frac { 1 } { 8 } t ^ { 4 } - 2 t ^ { 2 } + 4 t , \quad 0 \leqslant t \leqslant 4$$
- Find:
- \(\frac { \mathrm { d } y } { \mathrm {~d} t }\);
- \(\frac { \mathrm { d } ^ { 2 } y } { \mathrm {~d} t ^ { 2 } }\).
- Verify that \(y\) has a stationary value when \(t = 2\) and determine whether it is a maximum value or a minimum value.
- Find the rate of change of the depth of water, in metres per hour, when \(t = 1\).
- Hence determine, with a reason, whether the depth of water is increasing or decreasing when \(t = 1\).