Simple vector function problem, find slope of tangent?

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SUMMARY

The discussion focuses on the self-intersection of the curve defined by the parametric equations r = (t², t³ - t) at the point (1, 0). Participants confirm that the curve intersects itself at this point and clarify that to find the slopes of the tangents, one must evaluate dy/dx at the corresponding parameter values. The conversation emphasizes the importance of correctly interpreting the problem statement and applying calculus concepts to derive the slopes.

PREREQUISITES
  • Understanding of parametric equations in calculus
  • Knowledge of derivatives and the concept of dy/dx
  • Familiarity with self-intersecting curves
  • Basic skills in evaluating limits and continuity
NEXT STEPS
  • Study the evaluation of derivatives for parametric equations
  • Learn about self-intersection in curves and its implications
  • Explore techniques for finding slopes of tangents at specific points
  • Review examples of similar problems involving parametric curves
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Students studying calculus, particularly those focusing on parametric equations and tangent line analysis, as well as educators looking for examples of self-intersecting curves.

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Homework Statement



Show that the curve r = (t2,t3-t) Intersects itself at (1,0), and find the slopes of the tangents at this point.

Homework Equations





The Attempt at a Solution



Okay I can show it intersects itself there, but what I am having trouble with is when they say slopes of the tangents at this point .What do they mean? The wording sort of confused me.
 
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Hi rounded 2∏,
How did you show they intersect ?
I don't see anything wrong in the wording, so I just want to make sure you got it right from the beginning.
If you did, well, the slope is dy/dx which you should be able to evaluate simply at those two "events".

Cheers...
 

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