Let the parametric equations of a curve be x=2t+1

MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

Let the parametric equations of a curve be

x=2t+1,\qquad y=t^{3}-3t,

where

t\in[-3,3]

. (i) Obtain the expression for

\dfrac{dy}{dx}

in terms of

t

. (ii) Find all parameter values

t

in the given interval for which the tangent to the curve is horizontal. (iii) Determine the corresponding coordinate points on the curve.