Please help me understand this!!

Question

If a tank holds 4500 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as

V=4500(1-1/50t)2 0 ≤ t ≤ 50.

Find the rate (in gal/min) at which water is draining from the tank after the following amounts of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)

a) 5 min

? gal/min

b) 10 min

? gal/min

c) 20 min

? gal/min

d) 50 min

? gal/min

At what time (in min) is the water flowing out the fastest?

t=?min

At what time (in min) is the water flowing out the slowest?

t=min

Answer 1

For a,b,c and d, find dV/dt and substitute in the values of t.

For the minimum and maximum, find d²V/dt², set that to zero and solve for t. That will get you one value.

Then find v(t)=dV(50)/dt, which is an end point. The greatest of the two values is the maximum and the other is the minimum.