On a given day, the flow rate F (cars per hour) on a congested roadway is given by where v is the speed of the traffic in miles per hour. What speed will maximize the flow rate on the road? Round your answer to the nearest mile per hour.
A)12 miles per hour
B)16 miles per hour
C)23 miles per hour
D)19 miles per hour
E)17 miles per hour

Question

On a given day, the flow rate F (cars per hour) on a congested roadway is given by  where v is the speed of the traffic in miles per hour. What speed will maximize the flow rate on the road? Round your answer to the nearest mile per hour.
A)12 miles per hour 
B)16 miles per hour 
C)23 miles per hour 
D)19 miles per hour 
E)17 miles per hour

Quizplus · Accepted Answer

To find the speed that maximizes the flow rate, we need to find the maximum of the given function. Taking the derivative of the function with respect to v and setting it equal to 0, we get:

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Solving for v, we get v = 23 miles per hour. Therefore, the best choice is C.

On a Given Day, the Flow Rate F (Cars Per