(PLEASE ONLY COMPLETE PART 2, PART 1 IS COMPLETED AND IN THE WORD DOCUMENT, PLEASE USE THAT WORK AS A REFRERNCE TO WHAT NEEDS TO BE WRITTEN ABOUT )
For this Critical Thinking Assignment, you will be using the GeoGebra tool in Canvas to explore what it means to take the derivative of a function at a point. Part I: Complete the following steps: If you are not already familiar with GeoGebra, refer to this tutorial Links to an external site.. Using the GeoGebra tool in Canvas, input any non-linear function (such as a polynomial of degree 2 or higher, an exponential function or a trigonometric function). Click on “More” at the bottom of the tool menu to visualize all tools. Use the “Point” tool under “Basic Tools” to plot a point on the function you created. Create a tangent line at the point using the “Tangent” tool under “Construct.” First select the point, and then select the function graph it is on. Use the “Slope” tool under “Measure” by clicking on the point you created. Select the “Move” tool under “Basic Tools” and practice moving your point along the function graph you created. Save your GeoGebra work as a .pdf file for submission. Part II: Based on your work in Part I, discuss the following: Discuss any challenges that you face in visualizing the slope of the tangent line as you move the point along the graph. If necessary, adjust your function so that you can clearly see the value of the slope at all points along the curve shown in the graphing area. Discuss any observations you notice about how the slope of the tangent line changes as you move the point along the function graph. Pick three specific points on the graph. Give the coordinates of the point and the slope of the tangent line at each point. Discuss how the slope of the tangent line relates to the derivative at each point. At what point(s) does the tangent line become horizontal or vertical? What can you say about f(x), and f ’ (x) at those points? Based on your answer above, discuss how this animation is a visual representation of the derivative of a function at a point. Determine all points (if any) on your function graph for which the slope is 0. Discuss how this can be determined using only your GeoGebra animation and how it relates to the derivative of the function. Re-read section 3.1 in Calculus, Volume 1 to review the role of secant lines in relation to the derivative of a function. Research external resources that show ways to visually represent the limit definition of the derivative of a function at a point using secant lines. Make sure to include citations for the sources you used and to summarize your findings. Requirements: You must submit two files for this assignment. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in Part I. This file may be formatted as a numbered list of answers. Unless stated in the problem, a narrative discussion is not required, but you must provide enough information to show how you arrived at the answer. The second file should be a narrative paper, 2–3 pages in length, written in APA format, associated with the situation described in Part II. Specific requirements for the paper are provided below: Your paper should be 2–3 pages in length (not counting the required title page and references page). Cite and integrate at least two credible outside sources. The CSU Global Library is a great place to find resources. Your textbook is a credible resource. Include a title page, introduction, body, conclusion, and a reference page. The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic. The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment. The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs. Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required paper length excludes any tables, graphs, etc.) Document formatting, citations, and style should conform to the CSU Global Writing Center Links to an external site.. A short summary containing much that you need to know about paper formatting, citations, and references is contained in the New Sample APA Paper Links to an external site.. In addition, information in the CSU Global Library under the Writing Center/APA Resources tab Links to an external site. has many helpful areas (Writing Center, Writing Tips, Template Examples/Papers Essays, Figures and Tables, and others).