# 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