Consider the curve and for all real

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

Problem

Consider the curve

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

and

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

for all real

t

. At which of the following Cartesian coordinates does the curve have a horizontal tangent that is closest to the origin? (a)

(\sqrt{2},-4)

(b)

(0,0)

(c)

(-2,-3)

(d)

(0,-4)