Question

The volume of water in a container is x(2x^2 + x + 5)cm^3 when the depth is xcm. Water is added at a constant rate of 60cm^3/s when the depth is 5cm, at what rate is the level rising?

Answer 1

v = 2x^3 + x^2 + 5x

dv/dt = (6x^2 + 2x + 5) dx/dt
when x=5,
60 = 165 dx/dt
so dx/dt = 4/11 cm/s