Free ebookApplications of Derivatives: Optimization, Motion, and Curve Sketching

Course Description

Applications of Derivatives: Optimization, Motion, and Curve Sketching is a free ebook course in Basic studies that turns core Calculus ideas into practical tools for analyzing change and making better decisions. If you know the basics of limits and derivatives and want to use them with confidence, this course helps you move from rules to real problem solving.

You will learn how derivatives model change in contexts that matter, from interpreting how a quantity responds to inputs to identifying where a process improves or worsens. By working with critical points and increasing and decreasing behavior, you will build a reliable method for optimization that connects algebraic work to clear conclusions. You will also strengthen curve sketching by using concavity, second derivatives, and inflection points to predict the shape of a graph, then bring all derivative based features together into complete, accurate sketches that support interpretation.

The course also develops motion along a line, linking position, velocity, speed, and acceleration so you can read a situation mathematically and explain it in everyday language. You will practice related rates by translating word problems into equations, setting up relationships correctly, and differentiating with respect to time to connect changing variables. Optimization problems are approached as a modeling process, where you define the objective function, incorporate constraints stated in plain language, and interpret results with units, sensitivity awareness, and reasonableness checks.

To consolidate learning, you will work through mixed application sets with full solutions, reinforcing a progressive workflow that you can apply in exams, STEM courses, and real world analysis. Start the course now and use derivatives with clarity in optimization, motion, and curve sketching.