A curve is deﬁned by the parametric equations x=t^2 and y=t^3-3t ,
(a) Show that has two tangents at the point (3, 0) and ﬁnd their equations.
(b) Find the points on where the tangent is horizontal or vertical.
(c) Determine where the curve is concave upward or downward.
(d) Sketch the curve.

Question

A curve is deﬁned by the parametric equations x=t^2 and y=t^3-3t , 
(a) Show that has two tangents at the point (3, 0) and ﬁnd their equations.
 (b) Find the points on where the tangent is horizontal or vertical.
 (c) Determine where the curve is concave upward or downward. 
(d) Sketch the curve.

anonymous · Answer

I haven't dealt with tangent lines in ever. I remember the formula y-b = f'(a)(x-a) and I know I have to use  dy / dx = (dy/dt) / (dx/dt). So I know that at x = 3, t is +/- sqrt (3) and same with y, however y is 0 , +/- sqrt (3). After that I'm kinda lost.