The Calculus Toolkit: How Derivatives Explain Motion, Approximation, and Optimization

In this lecture, we explore calculus as a practical toolkit for understanding real-world systems. The lesson explains how derivatives help us track linked motion, estimate complex values using differentials, and find maximum or minimum points through optimization. This video covers: Related rates and linked motion Linear approximation and differentials Error propagation using derivatives Local and absolute extrema Critical points and the Extreme Value Theorem Real-world examples such as rocket tracking, water drainage, measurement error, and drone motion This lecture is useful for students learning calculus, engineering mathematics, AI mathematics, physics, and applied problem-solving.