Why a continuous curve can still be impossible to differentiate
In short: Just because a graph is connected doesn't mean it's smooth. This video explores the algebraic distinction between continuity and differentiability, showing why some functions fail the derivative test at specific points.
The video features Sal analyzing a piecewise function to determine its behavior at a shared edge point. While the function is continuous—meaning there are no breaks or jumps—it fails to be differentiable at that specific location.
This distinction is a core concept in AP Calculus AB. By examining these algebraic properties, students learn to identify points where a function lacks a defined slope, even when the path remains unbroken.
Opens the Intellect+ feed with this card first. Swipe up for the next one.
Sources
- Summary by Intellect · source: Differentiability at a point: algebraic (function isn't differentiable) | Khan Academy
To cite this card, link to https://intellectplus.co.uk/app/ideas-differentiability-at-a-point-algebraic-function-isn-t-differ.
How we source, check and correct cards: Editorial standards.
General information, not professional advice. Spotted an error? Flag the card or see corrections and complaints.
Intellect Plus is a visual educational discovery platform for exploring fascinating facts and ideas. Brain Food, Not Brain Rot. What is Intellect Plus?
Related
More in Mathematics · More in Ideas & Philosophy · Latest · A–Z · All topics
