Question

Find unit vectors that are parallel to the tangent line to the parabola y=x^2 at the point (2,4).

Answer 1

• The slope of the tangent line at the point is dy dx x=2 = 2x x=2 = 4 = 4 1 = rise /run . • A vector parallel to the tangent line is v = [1,4]
• A vector parallel to the tangent line is v = [1,4].
Two unit vectors parallel to the tangent line are u = v /|v| = [1,4]/ √ 1+16 = h √ -1/ √ 17 , 4 /√ 17 i and