The Limit Probe: Derivative Visualization

The Limit Probe: Derivative Visualization h Point P (x, f(x)) The Limit Probe Drag P to move, slide h to observe the limit. The Limit Probe: Derivative Visualization lets you explore this hands-on instead of only reading about it.

This unit introduces the derivative as the instantaneous rate of change. Students learn the formal definition of the derivative and the basic rules for differentiating common functions. It focuses on Defining the Derivative as a Limit, Instantaneous vs. Average Rate of Change, Differentiability vs. Continuity, The Power Rule, The Product and Quotient Rules, Derivatives of Trigonometric Functions from the “Unit 2: Differentiation: Definition and Fundamental Properties” section.

The sliders change the key inputs; you can drag elements directly on the canvas; the “Animate Limit”, “Reset” buttons 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 2: Differentiation: Definition and Fundamental Properties” 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 Defining the Derivative as a Limit, Instantaneous vs. Average Rate of Change, Differentiability vs. Continuity, The Power Rule, The Product and Quotient Rules, Derivatives of Trigonometric Functions — 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.