Calculus Workbook
Activity 2. In each of the following, you are given a description of a function f. Sketch a graph that matches
the description, and then indicate whether f, f', and f" are positive or negative.
(a) P = f(t) gives the population of a bacteria colony after t hours. The population
increases, and the rate at which the population grows also increases.
P
35
(b) H = f(t) gives the temperature in Fargo, North Dakota after t hours on a particular
day. The temperature is below zero the whole day, and although it steadily warms up
during the day, the rate of warming decreases with time.
H
t
t
