Chapter 15.2A, Problem 7GCE

To determine

To find out for what type of the function the methods described in the lesson guaranteed to give exact slope.

Answer to Problem 7GCE

Polynomial linear functions.

Explanation of Solution

The methods described in the lesson guaranteed to give exact slope for all the linear functions.

For example consider the following polynomial linear function −

  $y=2x^2;(1,2)$

To find the slope of the given function at required points do the following steps-

Step 1- Graph the equation $y=2x^2;$ .

Step 2- Use the window $[0,1]$ by $[2,3]$ so that the center is obtained.

Step 3- ZOOM feature will show the following result.

Step 4- Finally use the TRACE feature to know its slope.

  

The following is the slope of the given function using the $\frac{dy}{dx}$ feature of calculator.

  $\begin{array}{l}y=2x^2\\ \frac{dy}{dx}=4x\end{array}$

Substituting the values $x=1,x=2$ to find the slope of the function at these points.

  $\begin{array}{l}{\left(\frac{dy}{dx}\right)}_{x=1}=4\\ {\left(\frac{dy}{dx}\right)}_{x=2}=8\end{array}$