Chapter 15.2A, Problem 1GCE

To determine

To find out the slope of the graph of each function at the given point.

Answer to Problem 1GCE

  $(4,8)$

Explanation of Solution

Given:

  $y=2x^2;(1,2)$

Calculation:

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.

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