# Thread: sketching a plane curve

1. ## sketching a plane curve

Sketch the plane curve r(t)=<t^3,t^2>, find r'(1) and r''(1) , then sketch the position vector r(1), r'(1), r''(1) at the graph of the curve r(t)

2. ## Re: sketching a plane curve

To get a general idea of what the curve looks like eliminate the variable t.

$x=t^3 \quad y=t^2$ this gives

$y=x^{2/3}=\sqrt[3]{x^2}$

Recall that

$\frac{d}{dt}\mathbf{r}(t)=<\frac{dx}{dt},\frac{dy} {dt}>$

Give this a shot and try back if you are still stuck.

3. ## Re: sketching a plane curve

This is what I have so far. I am not sure how to sketch each of the position vectors.