A curve is defined parametrically by x = 3t - t^ 2

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

Problem

A curve is defined parametrically by

x = 3t - t^{2}, \\ y = 2t^{3} - 5t,

where

t \in \mathbb R

. Answer the following: (i) Find the value of

\dfrac{dy}{dx}

t = 2

. (ii) Hence obtain the equation of the tangent to the curve at the corresponding point on the curve.