# Thread: Help with parametric equations for tangent line

1. ## Help with parametric equations for tangent line

Consider the curve r (t) = < t + 2t^3, t + e^t >
Find parametric equations for the tangent line at (0, 1)

This occurs at t=0
dydt/dxdt = (1+e^0) / (1+6(0)^2) = 2/1 = 2

Am I doing this right?

(b) Find all t such that the tangent line is vertical.

2. ## ?

anyone?

3. Part a
$\displaystyle \begin{gathered} r(t) = \left\langle {t + 2t^3 ,t + e^t } \right\rangle \Rightarrow \quad r'(t) = \left\langle {1 + 6t,1 + e^t } \right\rangle \hfill \\ r'(0) = \left\langle {1,2} \right\rangle \hfill \\ l = \left\{ \begin{gathered} x = t \hfill \\ y = 2t + 1 \hfill \\ \end{gathered} \right. \hfill \\ \end{gathered}$

4. ## thx

is part b.) t=0?

5. No. a "vertical" vector must be of the form < 0, y>. When is the x component of the r' vector 0?

-1/6
thanks