Ahighway engineer wants to estimate the maximum number of cars that can safely travel on a particular road at a given speed. she assumes that each car is 14 feet long, travels at speed s, and follows the car in front of it at a safe distance for that speed. she finds that the number n of cars that can pass a given spot per minute is modeled by the function n(s)=86s14+14(s17)2 at what speed can the greatest number of cars travel safely on that road?
answer: a. 87 feet
1. you can find the t value of the vertex of the parabola as following:
2. substitute values:
3. substitute the vaue obtained into the equation given in the problem. therefore, you obtain the following result:
4. to the nearest foot: