Related Rates: The Falling Ladder Demo

This unit applies the derivative to real-world contexts, including related rates of change and particle motion. It also introduces L'Hôpital's Rule for evaluating indeterminate limits. Related Rates: The Falling Ladder Demo turns that idea into something you can manipulate directly and watch respond.

This unit applies the derivative to real-world contexts, including related rates of change and particle motion. It also introduces L'Hôpital's Rule for evaluating indeterminate limits. It focuses on Related Rates, Position, Velocity, and Acceleration, Linearization and Tangent Line Approximation, L'Hôpital's Rule, Local Linearity, Interpreting Derivatives in Context from the “Unit 4: Contextual Applications of Differentiation” section.

The sliders change the key inputs; you can drag elements directly on the canvas; the “Auto-Slide” button run actions or reset the demo. Every change updates the visualization in real time, so you can see exactly how each variable affects the outcome.

AP Calculus AB is a college-level course that explores the concepts of limits, derivatives, and integrals. Students learn to approach mathematical problems through multiple representations—graphical, numerical, analytic… This demo is the interactive piece for the “Unit 4: Contextual Applications of Differentiation” section. Open the full AP Calculus AB course wiki at https://www.getlykke.com/explore/public/ap-calculus-ab-c14bedc7-55ee-4bd3-99ff-a9a537a06a66 for notes, flashcards, quizzes and the other demos.

You'll build intuition for Related Rates, Position, Velocity, and Acceleration, Linearization and Tangent Line Approximation, L'Hôpital's Rule, Local Linearity, Interpreting Derivatives in Context — and, crucially, see how they behave when you change the inputs, which is hard to get from a textbook or lecture on AP Calculus AB alone.