Hi I have some vector function problems I'd like some help for, but I didn't see a forum for them so I'll start by posting one problem in case people don't know them.

I don't know all the english math terms so pardon me if the problem may seem like nonsense

I have a vector function, f(t)= (t^3-t, 3t+1).

I need to find all the cross points with the y-axis

All the points where the tangent is vertical

and all the tangents that are parallel with the line y=x

Thanks in advance and feel free to correct my math terms, be they wrong.