Curve sketching Question 10 Details
Since the volume of water flowing into the tank changes at a constant
rate, it is enough to plot the graph of H as a function of the
volume. For a given increase in the volume, the depth increases the
most when the tank is nearly empty and when it is almost full; it
increases the least when the tank is about half full. The rate of increase
of H decreases until the tank is half full and then increases
again until it is full. So the graphs should look something like those
below.
The red graph depicts H, its derivative is shown in green and
the second derivative in blue. These graphs are not accurate, but show the
general shape of the curves.