Let and for all real

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

Problem

Let

x(t)=t

and

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

for all real

t

. Determine the coordinates of every point of inflection of the curve. (a)

(\pm\sqrt{2},-4)

(b)

\left(\pm\dfrac{\sqrt6}{3},-\dfrac{20}{9}\right)

(c)

\left(\dfrac23,-\dfrac{128}{81}\right)

(d)

\left(\pm\dfrac{\sqrt6}{3},-2\right)