Finding Self-Intersection and Unit Tangent Vectors of γ(t)

[oddiseas]

Homework Statement

Show that the curve
γ(t)=(t²-t+1,t³-t)
has exactly one self-intersection point and finnd the two unit tangent vectors (in the direction of increasing t) at this point.

I have found the self intersection. I know that a unit tangent vector is the derivative of each component>But the wording has me a bit confused.What does it mean "in the direction of increasing t at this point"?

Homework Equations

The Attempt at a Solution

 

[Raskolnikov]

A tangent line to the curve extends in both directions (it has arrows on both ends).
In contrast, a vector extends in a single direction (only its head has an arrow).

You need to find the unit tangent in the direction of increasing t, not the opposite. Understand?