Related Rates: Videos & Practice Problems

A city's water pumping station operates based on the energy consumption model $E\left(t\right)=500t+\frac{1800}{\pi }\cos \left(\frac{\pi t}{6}\right)$, where $E\left(t\right)$ is the total energy in kilowatt-hour (kWh), and $t\ge 0$ is measured in hours from midnight. At what time of day does the energy consumption rate first reach its minimum? What is the minimum rate of energy consumption?