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.