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.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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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could you please do the sketch for 1d?

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