The motion of a point on a plane curve is described parametrically by and

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

Problem

The motion of a point on a plane curve is described parametrically by

x = t^2

and

y = t^3 - t

, where

t

is a real parameter. (i) Derive an expression for

\dfrac{dy}{dx}

in terms of

t

. (ii) Find the slope of the tangent to the curve at the point corresponding to

t = 1

. (iii) Determine the equations of both the tangent and the normal at this point in Cartesian form.