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)

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- Sep 17th 2012, 01:55 PMallstar2sketching 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)

- Sep 17th 2012, 06:14 PMTheEmptySetRe: sketching a plane curve
To get a general idea of what the curve looks like eliminate the variable t.

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

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

Recall that

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

Give this a shot and try back if you are still stuck. - Sep 17th 2012, 07:19 PMallstar2Re: sketching a plane curve
Attachment 24840

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