# Thread: Equation of the tangent line to r(t)=<t^3,t^2>

1. ## Equation of the tangent line to r(t)=<t^3,t^2>

I need help finding the equation of this tangent line at t=1, the point (1,1)

2. ## Re: Equation of the tangent line to r(t)=<t^3,t^2>

Originally Posted by allstar2
I need help finding the equation of this tangent line at t=1, the point (1,1)
The derivative of a vector valued function is

$\frac{d\mathbf{r}}{dt}(1)=\left< \frac{dx}{dt},\frac{dy}{dt}\right>\bigg|_{t=1}$

This will give you the tangent vector at the point (1,1)

Then use

$\mathbf{r}(1)$ and the tangent vector to find the tangent line

$\mathbf{T}(t)=\mathbf{r}(1)+t\left< \frac{dx}{dt},\frac{dy}{dt}\right>\bigg|_{t=1}$

Try this and if you get stuck post some work.