Find all points (if any) of horizontal and vertical tangency to the curve. use a graphing utility to confirm your results. (if an answer does not exist, enter dne.) x = t2 − t + 9, y = t3 − 3t

The horizontal tangents occur at: (9,-2) and (11,2)

The vertical tangent occurs at (8.75,-1.375)

See attachment

Step-by-step explanation:

The given parametric equations are:

and

The slope function is given by:

The tangent is vertical when

When , ,

The vertical tangent occurs at (8.75,-1.375)

The tangent is horizontal when

When t=1, ,

When t=-1, ,

The horizontal tangents occur at: (9,-2) and (11,2)