A traffic expert 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 18 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 $$N(s) = \frac{82 s}{18 + 18 \left(\displaystyle\frac{s}{23}\right)^2}$$ At what speed can the greatest number of cars travel safely on that road?

$s =$