Chapter 5.6, Problem 70ES

A traffic engineer monitors the rate at which cars enter the main highway during the afternoon rush hour. From her data she estimates that between $4:30\text{ P}\text{.M}\text{.}$ and $5:30\text{ P}\text{.M}\text{.}$ the rate $R\left(t\right)$ at which cars enter the highway is given by the formula $R\left(t\right)=100\left(1-0.0001t^2\right)$ cars per minute, where $t$ is the time (in minutes) since $4:30\text{ P}\text{.M}\text{.}$

(a) When does the peak traffic flow into the highway occur?

(b) Estimate the number of cars that enter the highway during the rush hour.