In this video I go over an example on using calculus to find the tangents to parametric curves. This example has multiple parts to it, and in this video I solve Part 1 which involves determining the equations of multiple tangents lines at one specific point on a parametric curve. This is possible for parametric curves because multiple values of the parameter can give the same x and y coordinates. This is one of the cool features of parametric equations which allows some very amazing graphs to be drawn up. In later parts of this example, I will show how to use calculus to manually draw the rest of this parametric curve, so stay tuned!
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Example:
A curve C is defined by the parametric equations: x = t2 , y = t3 - 3t.
a) Show that C has two tangents at the point (3, 0) and find their equations.
b) Find the points on C where the tangent is horizontal or vertical.
c) Determine where the curve is concave upward or downward.
d) Sketch the curve.
