MathDB

Consider a container of the shape obtained by revolving a segment of parabola

x = 1 + y^2

around the

y

-axis as shown below. The container is initially empty. Water is poured at a constant rate of

1\, \text{cm}^3

into the container. Let

h(t)

be the height of water inside container at time

t

. Find the time

t

when the rate of change of

h(t)

is maximum.

Problem Statement