The motion of a point in the plane is given by and .

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

The motion of a point in the plane is given by

x=t^{2}+t

and

y=t^{3}-3t

. (i) Obtain the expression for

\dfrac{dy}{dx}

in terms of

t

. (ii) Find all value(s) of

t

for which the tangent is horizontal. (iii) For each point found in part (ii), write the equation of the normal to the curve.