Derivatives of Vector Functions
One way to think of a curve in the plane (or in space) is as a collection of terminal points of vectors whose initial points are all at the origin. The vectors are given by a vector-valued function.
For example, the parabola shown at right can be thought of as the graph of the vector-valued function
I’ve created a Desmos demonstration that shows how graphs of vector-valued functions are related to their vectors (shown in blue), and how the derivative of a vector-valued function is related to both difference vectors and tangent vectors. You can access the demonstration here.
You can find more of my Desmos demonstrations here.
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