A collection of exercises centered around the graphical representation of functions, focusing on techniques learned in differential calculus and integral calculus, is readily available in portable document format. These exercises are typically accompanied by fully worked solutions, providing a valuable resource for students and educators alike. The problems generally require the application of concepts such as derivatives for finding critical points and intervals of increase/decrease, concavity, inflection points, limits, and asymptotes to produce an accurate sketch of a given function’s graph. An example would be sketching the graph of the function f(x) = x^3 – 3x^2 + 2, complete with identification of local extrema and inflection points, justified using the first and second derivatives.
The significance of practice problems, complete with solutions, lies in their contribution to a deeper understanding of calculus concepts and their practical application. Access to solved examples helps learners solidify theoretical knowledge and refine problem-solving skills. Historically, the development of calculus in the 17th century spurred the need for techniques to visually represent mathematical functions, making tools for graph analysis and sketching a crucial part of the curriculum. The availability of resources in a easily shareable format democratizes access to mathematical education.
