Question: A small cuboid box has a rectangular base of length 3x cm and a width x cm, where x>0. The height is y cm, where

A small cuboid box has a rectangular base of length 3x cm and a width x cm, where x>0. The height is y cm, where y>0. The sum of the length, width and height is 12cm.

Expression for y in terms of x: y=12-4x

Expression for V in terms of x: V=-12x^3+36x^2.

Find dV/dx
Find the value of x for which V is a maximum
Justify the answer to #2
Find the maximum volume .

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