Consider the curve 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

Consider the curve given by

x=t^{3}-3t

and

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

for all real

t

. For which values of

t

y

decreasing with respect to

x

? (a)

(-\infty,-\sqrt{2})\cup(1,\sqrt{2})

(b)

(-\sqrt{2},-1)\cup(0,1)\cup(\sqrt{2},\infty)

(c)

(-\infty,-\sqrt{2})\cup(-1,0)\cup(1,\sqrt{2})

(d)

(-\infty,-\sqrt{2})\cup(0,\sqrt{2})