Mathematics

Problem

For the vector-valued function

\mathbf{r}(t)=\langle f(t),g(t),h(t)\rangle

, which of the following conditions is sufficient to guarantee that

\mathbf{r}'(a)

exists? a)

f,\,g,

and

h

are continuous at

t=a

. b) Exactly one of

f,\,g,

h

is differentiable at

t=a

. c)

f,\,g,

and

h

are differentiable at

t=a

. d)

\displaystyle\lim_{t\to a}\frac{\|\mathbf r(t)-\mathbf r(a)\|}{t-a}

exists.