CPM Homework Help : CALC Problem 12-97

For the parametric curve with equations $x(t) = 2t^3 − 15t^2 + 24t + 7$ and $y(t) = t^2 +t +1$ , find all values of t at which the curve has a tangent line that is:

Horizontal

Vertical

Hint:

If the tangent line is horizontal, the $dy = 0$ .
If the tangent line is vertical, then $dx = 0$ .