Mathematics

Problem

Consider the curve given by

x=3t^{2}-6t

and

y=t^{3}-3t^{2}

. (a) Find

\dfrac{dy}{dx}

in terms of

t

. (b) Determine all values of

t

for which the tangent to the curve is horizontal. (c) Determine all values of

t

for which the tangent to the curve is vertical. (d) Find the slope of the tangent at the point corresponding to

t=1

and state whether the curve is rising or falling there.