Chapter 12.3, Problem 84E

To determine

To match: the function with the graphs of its derivative.

Answer to Problem 84E

Derivative of the function matches with the graph (a).

Explanation of Solution

Given information:

The graphs are labeled (a),(b),(c) and (d)

  

Given function

  $f\left(x\right)=1/x$

Calculation:

Consider the function $f\left(x\right)=1/x$

Use general power rule $\frac{d{x}^a}{dx}=a{x}^{a-1}$

The derivative of the function $f\left(x\right)=1/x$ is:

  $\begin{array}{c}{f}^{\prime }\left(x\right)=\frac{d}{dx}\left(\frac{1}{x}\right)\\ =-1x^{-1-1}\\ =-\frac{1}{x^2}\end{array}$

To graph of the function using graphing utility, use TI-83 calculator:

For this open the TI-83 calculator and press the $Y=$ button and enter the function in the form of $x,y$ as:

  

Now press the window button and change the scale as choice.

  

Now press the graph button and it will show the graph as:

  

This is the graph of derivative of the function $f\left(x\right)=\frac{1}{x}$ .

So, it matches with the graph (a).