Vectors and curve derivatives: tangent and higher-order change from a Cartesian

This example visualizes how vectors arise naturally from a Cartesian curve and its derivatives: by plotting the curve along with its first and second derivative objects, learners can see the geometric meaning of tangent direction and higher-order behavior. The key ideas are vector interpretation in geometry, the derivative as a directional/tangent quantity, and second derivatives as a measure linked to how the curve bends. Construction follows the GeoGebra command flow: CurveCartesian is used to define the curve γ, Derivative computes γ′ and γ″, and Point creates corresponding points such as M, M′, and M″. Vector-like objects (r, r′, r″) are then tied to these curve/derivative elements to emphasize how direction and variation evolve along the curve. Suitable for secondary advanced coursework and early university calculus/analytic geometry, especially when teaching the geometric meaning of derivatives.