In order to determine an appropriate delivery schedule to a group of rural homes in North Dakota, a fuel oil distributor monitors fuel oil consumption and the daily outdoor temperature (in degrees Fahrenheit). A table was constructed for a function F (T) of fuel oil consumption (in gallons per day) as a function of the temperature T.(a) Sketch a graph which you believe would approximate the graph of y = F (T).(b) What is the meaning of $F ^ { \prime } ( T ) ?$ What are its units?
(c) Write a sentence that would explain to an intelligent layperson the meaning of $F ^ { \prime } ( 0 ) = - 0.4$

Question

Quizplus · Accepted Answer

The Answer is (a) $(a) (There are many possible graphs, though presumably they are all decreasing!) (b) F ^ { \prime } ( T ) represents the rate of change of fuel oil consumption with respect to temperature. Its units are (gallons/day) / (<sup> \circ </sup>F). (c) F ^ { \prime } ( 0 ) = - 0.4 means that as the temperature increases past 0<sup> \circ </sup> F, the fuel consumption is decreasing by 0.4 (gallons/day) / (F).$
(There are many possible graphs, though presumably they are all decreasing!)
(b)

F ^ { \prime } ( T )

represents the rate of change of fuel oil consumption with respect to temperature. Its units are (gallons/day) / (^$\circ$F).
(c)

F ^ { \prime } ( 0 ) = - 0.4

means that as the temperature increases past 0^$\circ$ F, the fuel consumption is decreasing by 0.4 (gallons/day) / (F).

In Order to Determine an Appropriate Delivery Schedule to a Group