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

**allstar2** · September 23rd 2012, 07:20 PM

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

**TheEmptySet** · September 23rd 2012, 07:28 PM

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.

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

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