How do you find a unit vector a) parallel to and b) normal to the graph of f(x)=-(x^2)+5 at given point (3,9)?
Parallel unit vector:
Perpendicular unit vector:
Step 1: Determine the general equation for the slope of the tangent
The slope of a line is given by the derivative of the function.
the slope is
Step 2: Determine the specific slope of the tangent at the given point
So the slope is
Step 3: Determine the unit vector with slope of the tangent
Consider a unit vector with slope of
and since it is a unit vector:
Unit vector parallel to the tangent:
Step 4: Determine the unit vector perpendicular to the tangent
Remember that if a line has a slope of
So we are looking for a unit vector with slope
Using the same logic as in Step 3, we have