The reaction of the body to a dose of a certain drug is such that for . Sketch the graph of as a function of . If the sensitivity is the rate of change of and , find for what value of is the sensitivity is a maximum.
Source: Rosenberg, R.L. (1984). Elementary Calculus: Course Notes. Ottawa, Canada: Holt, Rinehart and Winston. (Exercise 2: Question 12, p. 11)