In an optimisation problem, we generally use differentiation to find the largest or smallest possible value of some function. The function under question usually arises from a modelling situation.

As you will see, when there are many variables in the problem, the given information can often be used to eliminate some variables, giving us an easier problem.

A closed, square-based cuboid is to be constructed out of $200{\text{cm}}^2$ of sheet metal.

Find the maximum possible volume of the cuboid.