A water tank is connected to a pump whose operation over the first hours can be…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A water tank is connected to a pump whose operation over the first 5 hours can be modelled by the volume function
V(t)=t3−6t2+9t+1,
where V(t) is the volume of water (in cubic metres) present in the tank t hours after the pump is switched on. Analyse the behaviour of the tank during this period.
(i) Find all critical points of V(t) in the interval 0≤t≤5.
(ii) Determine on which sub-intervals the volume of water in the tank is increasing and on which it is decreasing.
(iii) Identify the exact times at which the tank contains a local maximum or a local minimum volume within the given interval, and calculate these volumes.
(iv) State, with reasons, whether the tank ever starts emptying after it has begun filling, and indicate the practical significance of your conclusion.