Final answer:
The unit vector parallel to the tangent line of the parabola y = x² at the point (6, 36) can be found by finding the slope of the tangent line.
Step-by-step explanation:
Unit Vector Parallel to Tangent Line of Parabola
To find a unit vector that is parallel to the line tangent to the parabola y = x² at the point (6, 36), we need to find the slope of the tangent line at that point.
The derivative of y = x² is dy/dx = 2x. Substituting x = 6 into the derivative equation, we get dy/dx = 2*6 = 12.
Therefore, the slope of the tangent line at the point (6, 36) is 12. Now, we can find the unit vector with this slope as its direction.