Problem 30
Page 308
Section 4.6: Optimization Problems
Chapter 4: Applications of Differentiation
Given information
The graph shows the fuel consumption of a car (measured in gallons per hour) as a function of the speed of the car. At very low speeds the engine runs inefficiently, so initially decreases as the speed increases. But at high speeds the fuel consumption increases. You can see that is minimized for this car when . However, for fuel efficiency, what must be minimized is not the consumption in gallons per hour but rather the fuel consumption in gallons per mile. Let’s call this consumption .
Step-by-step explanation
According to the question, We can draw the diagram of a graph which is shows the fuel consumption of a car (in gallons per hour) as a function of the speed of the car. At very low speeds the engine runs inefficiently, so initially decreases as the speed increases. But at high speeds the fuel consumption increases. You can see that is minimized for this car when . However, for fuel efficiency, what must be minimized is not the consumption in gallons per hour but rather the fuel consumption in gallons per mile. Let’s call this consumption .
So,