Show that the parametric curve given by x = t^2 + 1, y = t^3 - 2t intersects itself at the point (x,y) = (3,0) by finding two different values of t that give this point on the curve. 1b) Find the equations of the two tangent lines to the curve at this point. 1c) Identify coordinates of points on the curve with (i) a horizontal tangent (ii) a vertical tangent.
Show that the parametric curve given by x = t^2 + 1, y = t^3 - 2t intersects itself at the point (x,y) = (3,0) by finding two different values of t that give this point on the curve. 1b) Find the equations of the two tangent lines to the curve at this point. 1c) Identify coordinates of points on the curve with (i) a horizontal tangent (ii) a vertical tangent.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section: Chapter Questions
Problem 18T
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Please do the following questions with full working
1a) Show that the parametric curve given by x = t^2 + 1, y = t^3 - 2t intersects itself
at the point (x,y) = (3,0) by finding two different values of t that give this point
on the curve.
1b) Find the equations of the two tangent lines to the curve at this point.
1c) Identify coordinates of points on the curve with (i) a horizontal tangent (ii) a
vertical tangent.
1d) Sketch the curve showing its orientation.
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