Question

tangents at the point of intersection

Answer 1

A curve in xy plane is defined in parametric form :
\[x = f(t); y = g(t)\]

It is given that the curve intersects with itself at point \(\large (x_1, y_1)\). Is there a way to get the slopes of tangents at this point ?

Answer 2

Clearly the first derivative would be undefined at \(\large (x_1, y_1)\). im bit clueless on how to approach this :/

Answer 3

whats the function anyway ?

Answer 4

some general function in parametric form

Answer 5

this remineds me with some curve

Answer 6

ok in this case , yes there is a tangent but not unique for the curve ( im not sure if you could name it tangent of thecurve ) how ever to get rid of this proplem define a piecewise function for two intervals

Answer 7

f1