The activity Wake Up! described the Cazneau family’s consumption of coffee. The function f (d) = 30 – 0.14d gives a good approximation of the amount of coffee (in pounds) the Cazneau family had left after d days.
For this question, treat this as a continuous function, rather than as a discrete function. That is, assume d need not be a whole number.
a. Because f (5) = 29.3, the graph of this function goes through the point (5, 29.3). What is the derivative of the function at this point?
b. What does your answer tell you about the rate at which the Cazneaus drank coffee?
c. Pick a point on the graph of the function other than(5,29.3). Find the derivative at that point.