SOLUTION: The volume of water in a tank at a particular time (measured in seconds) is given by V (t) = 5t(2 − t) m3 . Find the rate of change of the volume of water in the tank from fir

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Question 1202240: The volume of water in a tank at a particular time (measured in
seconds) is given by V (t) = 5t(2 − t) m3
. Find the rate of change of the
volume of water in the tank from first principles (using the definition of the rate
of change).

Found 2 solutions by ikleyn, math_tutor2020:
Answer by ikleyn(52864) (Show Source):
You can put this solution on YOUR website!
.

It is about finding the derivative of the given function,

and usually people solve such problems using standard rules of Calculus,

without using "first principles".

Answer by math_tutor2020(3817) (Show Source):
You can put this solution on YOUR website!

The term first principles in this context refers to the limit definition of the derivative.

Let's first determine V(t+h).

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Then we can compute the derivative to get the instantaneous rate of change.

The instantaneous rate of change of the volume is V'(t) = 10-10t
The units for the rate of change is "cubic meters per second".

Extra info:
1 cubic meter = 1000 liters = 1 kiloliter
1 meter = 3.2808 feet approximately
1 cubic meter = (3.2808)^3 = 35.313 cubic feet approximately