### Home > APCALC > Chapter 12 > Lesson 12.2.2 > Problem12-86

12-86.

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

1. horizontal

2. vertical

$\text{The slope of the tangent line is }\frac{dy}{dx}=\frac{y^\prime(t)}{x^\prime(t)}.$

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