Curve sketching is the great synthesis exercise of the fifth year: putting differential calculus to work to draw the qualitative graph of a function without a calculator. Here the derivative is not computed as an exercise in itself, but is used as a tool. Starting from relative maxima and minima (necessary condition and first-derivative test) one moves on to absolute maxima and minima with the table method, then to the curvature of the graph with the second derivative (convexity, concavity, inflection points). Everything converges into the six-step scheme of the complete study — domain, limits and asymptotes, sign, first derivative, second derivative, graph — finally applied also to functions depending on a parameter, typical of the school-leaving exam.
Sections
- Relative maxima and minima
- Absolute maxima and minima: the table method
- Convexity, concavity and inflection points
- Complete curve sketching: the six steps
- Curve sketching with a parameter