Chapter 15.2A, Problem 9GCE

To determine

To approximate the slope of the curve at several different points.

Explanation of Solution

Given:

  $y=e^x$

Calculation:

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

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

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.

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

Substituting the values $x=1,x=0$ to find the slope of the function at these points.

  $\begin{array}{l}{\left(\frac{dy}{dx}\right)}_{x=1}=e\\ {\left(\frac{dy}{dx}\right)}_{x=0}=1\end{array}$

Since the function is exponential the slope can’t be found upon zooming also as it is only valid for linear functions.