A curve is given by the parameterization and for

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

Problem

A curve is given by the parameterization

x=u^{2}

and

y=\dfrac{u^{3}}{3}

for

0\le u\le 2

. Which of the following expressions equals the speed

\lVert\mathbf r'(u)\rVert

of the particle? (a)

\sqrt{u^{2}+4}

(b)

u^{2}(u^{2}+4)

(c)

u\sqrt{u^{2}+4}

(d)

\sqrt{u^{2}+2u}