Tangent lines for a curve using gravity

thingiverse

This is a manipulative tool that showcases tangent lines intersecting a curve by adjusting rectangular "tangent line" blocks placed on top of a point along the curve as depicted in the initial two images. Clearly, this concept falls short at an inflection point since, in these instances, the tangent line cuts through the curve entirely. To overcome this limitation, we have introduced a 'secant line/tangent line' component that slots seamlessly into the curve at any given inflection points, as visualized in the third picture. This model can also be used to demonstrate key theorems and their accompanying proofs such as Rolle's Theorem in its fourth depiction or utilizing it to prove the Mean Value Theorem via Rolle's Theorem, resulting in a comprehensive illustration found in the final image.