Homework Soursein a study of traffic control the number n of vehicles on a
in a study of traffic control, the number n of vehicles on a certain section of a highway from 2pm to 8 pm, was found to be n = 200(1 + r^3e^-1). Where t is the number of hours after 2 p.m. At what time is the number of vehicles the greatest? If you could explain how you got the answer that would help, thankyou.
Solution
what you have to do is to find the maximum of the equation. To do this you take the derivative and then set it equal to 0. Then you should take the 2nd derivative to ensure that it is a maximum and not a min, so the 2nd derivative should be negative for a max. dn/dr= 200(3e^-1*r^(-1+3e^-1)) when you set it equal to zero theres is no solution http://www.wolframalpha.com/input/?i=maximum+of+y%3D+200*%281%2Br%5E%283e%5E-1%29%29 the function is always increasing so the maximum is at 8pm
