{Use of Tech} Flow from a tank A cylindrical tank ​​is full at time t=0 when a valve in the bottom of the tank is opened. By Torricelli’s law, the volume of water in the tank after t hours is V=100(200−t)², measured in cubic meters.
d. At what time is the magnitude of the flow rate a minimum? A maximum?  

Verified step by step guidance

1. First, differentiate the volume function V(t) = 100(200 - t)² with respect to time t to find the flow rate, which is given by the derivative dV/dt.
2. Next, apply the chain rule to differentiate the function: dV/dt = 100 * 2(200 - t)(-1).
3. Simplify the expression for the flow rate to get dV/dt = -200(200 - t).
4. To find the critical points where the flow rate is at a minimum or maximum, set the derivative dV/dt equal to zero and solve for t.
5. Finally, analyze the second derivative or use the first derivative test to determine whether the critical points correspond to a minimum or maximum flow rate.