textbook-theory · English
Implicit Functions
A five-page calculus lecture note covering the definition and properties of implicit functions, with worked examples drawn from conic sections (ellipses, parabolas, hyperbolas). The note develops the technique of implicit differentiation — treating y as a function of x, differentiating both sides of a relation, and solving for y′ — and identifies 'bad points' where the derivative formula is undefined, corresponding to vertical tangents.
implicit functionsimplicit differentiationconic sectionscalculus