1. The problem statement, all variables and given/known data A curve C is defined by the parametric equation x=t^2, y=t^3-3t. 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 2. Relevant equations y-y1=m(x1-x), (dy/dt)/(dx/dt)=m, when dy/dt=0 and dx/dt ≠ 0 there is a horizontal tangent at f(t),g(t), and vice versa for vertical tangents 3. The attempt at a solution a) @ (3,0) 3=t^2, t= ±√3, 0=t^3-3t @ ±√3 and @ 0 but since 0 doesnt agree with x=t^2 we just stick with ± √3 (dy/dt)/(dx/dt)= 3t^2-3/2t @√3 3(√3)^2-3/2√3= 6/2√3= √3=m y-0=√3(x-3), y=√3x-3√3= tangent @ √3 3(-√3)^2-3/2(-√3)= -12/-2√3= 2√3=m y-0=2√3(x-3), y=2√3x-6√3=tangent @-√3 End part A B) dx/dt=2t=0 when t=0, dy/dt=3t^2-3 ≠0 thus vertical tangent @ f(0), g(0)= (0)^2, (0)^3-3(0)= 0,0 dy/dt=3t^2-3 =0 when t= 1 but dx/dt=2t ≠ 0 false so no horizontal tangent. End part B. That is my attempt at solving the problem. Any comments on what I did wrong or just telling me if I'm right is helpful. Thank you for your time.