Visualizing change: how a function's shape dictates its derivative

Ideas & Philosophy · Published 1 November 2026 Swipe more like this →

In short: Understanding calculus often feels abstract until you see it visually. This video explores the direct graphical relationship between a function and its derivative, showing how the behavior of one determines the geometry of the other.

Sal Khan demonstrates how to sketch the graph of a derivative based on the visual properties of an original function. By observing where a function rises, falls, or levels off, students can predict the corresponding values and shapes of its derivative.

The lesson provides a foundational framework for AP Calculus AB, helping learners move beyond rote calculation toward a conceptual mastery of how rates of change manifest in geometry.

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