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If given a maximum capacity of tank and Flow in equation and Flow out equation.There some initial volume of water. How can we calculate the maximum amount of volume at a given time (second).How can we calculate what is the maximum volume at a given time (seconds).

[Walter Roberson]

net flow is the difference between flow in and flow out.

initial volume + integral(net flow) = resulting volume

This leads to the equation integral(net flow) = (resulting volume - initial volume)

For maximum volume over a given time, you do a standard calculus maximization calculation: that the maximum must correspond to either one of the endpoints (t + epsilon) or (10 minus epsilon), or else it must be at one of the inflection points where the derivative of the net flow is 0. So calculate the derivative, solve for zeros, then use the double-derivative test to check for whether each of the solutions is a maximum or minimum. Standard stuff, so you should be good to go.

[Image Analyst]

Max at a given time? Wouldn't a given time just have one volume? The volume is whatever it is, say 1000 liters. How can the given time (say t = 42 seconds) have a max volume, a min volume, and some in-between volumes? I can see the max volume over all times and finding what time the max volume occurs at , but not the max at a certain, specific time because a given time (say 42 seconds) has only one volume , say 1000 liters or whatever.

And this is the fifth question since September 6 on this problem? What's up with that???? Why 5 separate posts over 4 weeks?