Demography of Drosophila (fly)

When a population is growing in a closed system you can observe that at the beginning its size is increasing slowly. This is because there are too few flies to procreate. After a while the population grows at a faster rate because the number of flies sexualy mature has increased sufficiently. However, resources become scarce rapidly, there is less room for each drosophila, less food, etc. Hence the growth of the population is slowing down and eventually it reaches the carrying capacity (the carrying capacity is the maximum population size that can be supported indefinitely by a given environment. The carrying capacity is achieved through a trade-off of birth and death rates).

This situation is described by a mathematical function which graph (shown hereunder) shows the growth of a drosophila population as a function of the time:

You are asked to:

a) Sketch the graph of the derivative of the hereabove curve. Which units are you going to use for the x and the y-axis ?

b) Find the days during which the population grows at the fastest and at the slowest rate.

Note: to answer this math problem, you must print the graph. If you do not have a printer at home, you can transfer the parabola on a thin sheet of paper applying it on your screen and using a pen to copy the curve, the x and y-axis by transparency.