The plane curve is given by and for all real

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

Problem

The plane curve is given by

x(t)=t^{3}-6t

and

y(t)=t^{2}-4

for all real

t

. For which value of

t

does the curve have a horizontal tangent line? (a)

t=\sqrt{2}

(b)

t=0

(c)

t=2

(d)

t=-\sqrt{2}