Calculus

Curve sketching and families of functions

Building blocks, full analysis by function class, parameter families and reconstruction

Final two years of upper secondary school and exam preparation, basic and advanced level.

First the building blocks: domain and symmetry, zeros, monotonicity and extrema, curvature and inflection points, behaviour at infinity and asymptotes. Then the complete analysis by function class — polynomial, rational, exponential, logarithmic and trigonometric functions. This is followed by families of functions (zeros and extrema depending on the parameter, loci, common points, parameters from conditions, integrals with parameters) and function reconstruction. The chapters Application, Abitur, Transfer and Abitur+ raise the level step by step. Every problem comes with two hints, an approach, the full solution and the typical mistake.