# Math Help - help with word problem?

1. ## help with word problem?

The number of liters of water remaining in a tank t minutes after the tank has started to drain is R(t)=2t^3-20t^2-72t+820. At what moment is the water draining the fastest?

the first thing i think of is to take the derivative but then after that i dont know what to do.

i took 2nd derivative then set it to 0
then i get
x= 10/3

2. The derivative gives you the rate of change of the water volume.
You want to find the maximum value of this change.
Hence you must calculate the 2nd derivative and set it to zero.

3. Originally Posted by yoman360

the first thing i think of is to take the derivative but then after that i dont know what to do.
You need to find where the gradient function is a max, therefore take the derivative again, set it to zero and solve for t.