For the vector-valued function

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

\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.