How do you find a unit vector (a) parallel to and (b) normal to the graph of f(x) at the indicated points given function: #f(x) = sqrt(25+x^2)# and point: (3,4)?
1 Answer
Jul 26, 2018
Unit vector parallel to the graph at (3,4) is is
Unit vector normal to the graph at (3,4) is is
Explanation:
slope of the tangent indicates a vector parallel to the graph at a point
Differentiating
Let
Squaring both sides
Now, Applyig chain rule and differentiating
At
Slope of a parallel line is
Unit vector parallel to the graph at (3,4) is is
Normal is perpendicular to the parallel.
Thus, slope of the normal is
Slope of anormal line is
Unit vector normal to the graph at (3,4) is is