Derivative at curve endpoints

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Suppose that ${\bf R}(s)$ is a curve in 3D space parameterized by arc length $s$. The curve has endpoints at $s=0$ and $s=S$. Can one give meaning to and calculate $\frac{d{\bf R}(s)}{ds}$ and $\frac{d^2{\bf R}(s)}{ds^2}$ at $s=0$ and $s=S$?