Uses of the Derivative Question U1 Let P(t) model the population of the country, in thousands, t years after 2000; let R(t) model the number of doctors in the country, in thousands, t years after 2000 P(t) What is the significance of R(t) ? Can P(t) ever be negative? Why/why not? Assume P'(t) exists for all t. Can P'(t) ever be negative? Why/why not? d ( P(t) Find an expression for dt R(t) / . Assume all required derivatives exist. P(t) Suppose P(t), P'(t), R(t), and R'(t) are always positive. Is it possible for dt R(t) / to be negative? If possible, give a set of positive values P(t), P'(t), R(t), R'(t) that would accomplish this; if not possible, explain why not. Suppose your goal is to improve medical care in the country (by increasing access to doctors, d ( P(t) for example). Do you want dt R(t) / to be positive or negative? Explain why