Find the unit vector tangent to the curve y = x^4 at the point(x,y) = (1,1).

Answer 1

dy/dx = 4x^3
at (1,1), dy/dx = 4
equation of tangent : y-1 = 4(x-1)
y = 4x -3
we already have one point on this, (1,1)
another point: let x = 2, y = 5
direction vector of that tangent = < 2-1, 5-1> = < 1,4>
so a unit vector would be <1/√17 , 4/√17>