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

By | November 4, 2016

Addendum: Derivative of f(x)=9/x

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.