Exercises 123 and 124 are about the accompanying graphs. The graphs in part (a) show the numbers of rabbits and foxes in a small arctic population. They are plotted as functions of time for 200 days. The number of rabbits increases at first, as the rabbits reproduce. But the foxes prey on rabbits and, as the number of foxes increases, the rabbit population levels off and then drops. Part (b) shows the graph of the derivative of the rabbit population, made by plotting slopes.
a. What is the value of the derivative of the rabbit population when the number of rabbits is largest? Smallest?
b. What is the size of the rabbit population when its derivative is largest? Smallest (negative value)?
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