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A
derivative of a space curve can be taken as well, following the same rules as
before (only now involving vectors).

The derivative is** x1 – x0**.

The derivative of a space curve provides a vector*tangent* to
the curve. It provides a vector showing
which way the curve is going.

The derivative is

The derivative of a space curve provides a vector

High

Exercise

Derive a mathematical expression for the derivative (tangent) of the following cubic space curve, where

What is the derivative evaluated at t = 0?

What is the derivative evaluated at t = 1?

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