3 ideas
The book builds toward constrained optimization (Lagrange multipliers) as the mathematical form of rational choice under scarcity. Most economic models reduce to maximizing an objective subject to constraints.
Derivatives let economists ask how an equilibrium shifts when a parameter changes, formalizing 'what happens if.' The sign of a partial derivative encodes an economic prediction.
The text insists on defining functions, limits, and continuity precisely before deploying them in models. Sloppy math yields misleading economics, so the tool is taught for its own sake first.