The marginal cost for Quest can be modeled by the function: C'(t)=-3(t^2-8t+12) in millions of dollars per year. Here, t=0 corresponds to the year 1980.
a. Graph the marginal cost function between the years 1980 and 1990.
b. Find and interpret the meaning of the points on the graph where t=5, t=6
c. What can you say about C'(t) between the years 1982 and 1986? What does that mean in the context of the problem? What is happening in 1984?
d. Find the slope of the line tangent to your graph at t=3. Interpret and give the units. (keep in mind that the function you are looking at is not the cost but the marginal cost)
e. Based on the graph, which year is the marginal cost the highest? What does this say about the cost during this year?
f. Before going on, explain clearly how to find a local maximum or minimum of a function. Now, by looking at the graph, when is the cost (not the marginal cost) possibly the lowest?
g. Use the graph of the marginal cost to sketch a possible graph for C(t).
h. Find and interpret (d^2 C)/(dt^2)| d=6 Give the units. You are welcome to use C'(6) in your interpretation.