# Calculus – Addendum: Derivative of f(x)=9/x Find the equation of the Tangent Line at x = 3

By | November 4, 2016

In this tutorial the students will learn how to use the power rule to find the derivative, create the equation of the tangent line and verify the results with the TI-84 graphing calculator.

## Explicit Function

$f(x)=\frac {9}{x}$

## Point of Tangency

Substitute in the value of x, 3, into the function to find the value for y.

$y=f(3)=\frac {9}{3}=3$

The point of tangency is (3,3).

## Derivative

$f'(x)=\frac {-9} {x^2}$

Now substitute in the point of tangency, (3,3), to find the slope of the tangent line.

$f'(3)=\frac {-9} {3^2}=\frac {-9}{9}=-1$

## Point Slope Formula

Substitute in the values for the slope, -1, and the point of tangency, (3,3), into the following formula.
$y-3=-1(x-3)$
$y-3=-1x+3$
$y=-1x+3+3$
$y=-x+6$

## Graphing Tool

Click on the link below to open an interactive online graphing calculator to view this graph.