Not really sure what else to call this question, and equally as unsure where I got it from, but it is a typical differentiation question so I thought it would be worthwhile to go through it.


An engineer is given a piece of sheet metal and is asked to construct a tank with a depth of "x" centimetres such that the volume of the tank is at its maximum. In other words, there is an optimum depth, or value for "x" which will maximise the volume of the tank. The dimensions of the sheet of metal are as given. 


Find the optimum value for the depth of the tank.




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