3 The volume, \(V \mathrm {~m} ^ { 3 }\), of water in a tank after time \(t\) seconds is given by
$$V = \frac { t ^ { 3 } } { 4 } - 3 t + 5$$
- Find \(\frac { \mathrm { d } V } { \mathrm {~d} t }\).
- Find the rate of change of volume, in \(\mathrm { m } ^ { 3 } \mathrm {~s} ^ { - 1 }\), when \(t = 1\).
- Hence determine, with a reason, whether the volume is increasing or decreasing when \(t = 1\).
- Find the positive value of \(t\) for which \(V\) has a stationary value.
- Find \(\frac { \mathrm { d } ^ { 2 } V } { \mathrm {~d} t ^ { 2 } }\), and hence determine whether this stationary value is a maximum value or a minimum value.
(3 marks)