Let x=t^3-3t

y=t^2-t

Where is the tangent parallel to the x-axis? y-axis? line y=x?

The curve intersects itself once. Find this point.

Thanks.

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- Apr 25th 2009, 03:14 PMzhupolongjoeParametrics.....
Let x=t^3-3t

y=t^2-t

Where is the tangent parallel to the x-axis? y-axis? line y=x?

The curve intersects itself once. Find this point.

Thanks. - Apr 25th 2009, 03:22 PMTheEmptySet
Horizontal tangents occur when $\displaystyle \frac{dy}{dt}=0$

Vertical tangents occur when $\displaystyle \frac{dx}{dt}=0$

to find the derivative use the formula

$\displaystyle \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}= \frac{2t-1}{3t^2-3}$

For the last here is a hint.

For what values of t will the function have the same y-coordinate.

Find these and compare those times with the x -coordinate.