Consider the parametrically defined curve and for all real

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Consider the parametrically defined curve

x=\dfrac{t^{2}-4}{t^{2}+1}

and

y=t^{3}-t

for all real

t

. At which point does this curve have a vertical tangent line? (a)

\left(-\dfrac{11}{4},-\dfrac{2}{3\sqrt{3}}\right)

(b)

(-4,0)

(c)

(0,-4)

(d)

\left(-\dfrac{3}{2},0\right)