Chapter 11.3, Problem 13E

To determine

To evaluate: the graph of the function and tangent line at the point $\left(1,f\left(1\right)\right)$ and use the graph to approximate the slope of the tangent line.

Answer to Problem 13E

  

The slope of tangent line is $-\frac{1}{4}$ .

Explanation of Solution

Given:

  $f\left(x\right)=\frac{1}{x+1}$

Using the graphing calculator to plot the graph,

  

The blue line shows the tangent line at the point $\left(1,f\left(1\right)\right)$ .

So, it can be seen that the slope of tangent line is $-\frac{1}{4}$ .