5 The volume \(V \mathrm {~m} ^ { 3 }\) of a pile of grain of height \(h\) metres is modelled by the equation
$$V = 4 \sqrt { h ^ { 3 } + 1 } - 4$$
- Find \(\frac { \mathrm { d } V } { \mathrm {~d} h }\) when \(h = 2\).
At a certain time, the height of the pile is 2 metres, and grain is being added so that the volume is increasing at a rate of \(0.4 \mathrm {~m} ^ { 3 }\) per minute.
- Find the rate at which the height is increasing at this time.