Final answer:
To find the cheapest driving speed, calculate the total cost per mile by adding chauffeur cost and fuel cost, then minimize this function with respect to speed.
Step-by-step explanation:
To find the cheapest driving speed for a limousine that has a fuel efficiency of m(v) = (120 − 2v)/6 miles per gallon at speed v (in mph), we need to calculate total cost of driving, which includes both fuel cost and chauffeur cost.
The chauffeur cost per mile is constant at $16/h. The fuel cost per mile can be calculated as the inverse of the fuel efficiency times the cost of gas $4.50/gal. To find the total cost per mile, we add the chauffeur cost per mile to the fuel cost per mile.
We must formulate this as a function of speed v, then find its minimum, which will give us the cheapest driving speed. To find the minimum of this function, we set its derivative with respect to v to zero and solve for v.