Tangent lines for a curve using gravity

This is a calculus manipulative that demonstrates tangent lines to a curve by balancing the rectangular 'tangent lines' off of a point on the curve as shown in the first two pictures (the shorter 'tangent line' is for tighter spots on the curve). Of course this is impossible at an inflection point since there the tangent line passes through the curve. Therefore, we have added a 'secant line/tangent line' that slots into the curve at one of the inflection points as shown in the third picture. The model can also be used to illustrate theorems and their proofs such as Rolle's Theorem (fourth picture) or the proof of the Mean Value Theorem using Rolle's Theorem (last picture).