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This problem is well suited for those who are about to begin to learn the concepts of calculus. It is easy to access, yet offers many insights into the relationships between functions and their derivatives. The language of calculus - change, derivative, turning points, maximum, minimum, curve, functions, equations, axes, zeros, continuity etc. - should naturally arise in the exploration of this task and it should provide a natural framework onto which to build the formality of calculus at a later date.