The trajectory of a point in the plane is given by and for .
MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions
Problem
The trajectory of a point in the plane is given by x=3t−t3 and y=3t2+1 for −2≤t≤2.
(i) Determine all real values of t in the given interval for which the tangent to the curve is vertical.
(ii) Find the corresponding coordinate points on the curve.
(iii) State how many distinct vertical tangents the curve possesses in the stated interval.