- #1

A.Magnus

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The parametrization of the curve represented by the vector-valued function

$$\textbf{r}(t) = f(t)\textbf{i} + g(t)\textbf{j} + h(t)k$$

is smooth on an open interval $I$ when $f'$, $g'$ and $h'$ are continuous on $I$ and $\textbf{r}'(t) \neq \textbf{0}$ for any value of $t$ in the interval $I$.

Can somebody please tell me why is that $\textbf{r}'(t)$ has to be not equal to zero? Thank you beforehand for your time and gracious helping hand. ~MA