how to find the vector that tangent to the parabola y=x^2 at (2,4) ??
It will be a 2D vector, and parallel to the line defined by the tangent at that point.
To find the tangent, which will be of the form , to find , take the derivative, then evaluate the derivative at that point.
.
Thus .
We have
We also have as a point on the tangent.
So
.
Thus the tangent is .
So you will have a vector that is parallel to and that passes through .
Can you go from here?