Introduction
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Above we see bubble magician Tom Noddy produce a "tetrahedral bubble" within a system of bubbles. All the phenomena one observes in the bubble image above (e.g. angles, edge and face configurations) are governed by a minimum principle.
This chapter puts the concept of the derivative to work. The first and second derivatives are used to analyze functions and their graphs.
In particular, we begin our study of maxima and minima in calculus which ultimately leads to the mathematical theory explaining bubble configurations as the one seen in the picture.
Newton’s Method in Section 4.8 employs the derivative to approximate solutions of equations.
In Section 4.9, we introduce antidifferentiation, the inverse operation to differentiation, to prepare for the study of integration in Chapter 5.