Chapter 11, Problem 57CR

To determine

To evaluate: the graph of f at the point (2, f (2)) and then use it to find the slope of the tangent at the point.

Answer to Problem 57CR

  

The slope is $-\frac{3}{2}$ .

Explanation of Solution

Given:

  $f\left(x\right)=\frac{6}{x-4}$

Using the graphing calculator to graph the given equation,

  

Taking the two points to find the slope,

  $\left(0,0\right)$ and $\left(2,-3\right)$

  $\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-3-0}{2-0}\\ =-\frac{3}{2}\end{array}$

The slope is $-\frac{3}{2}$ .