There is part 1 and part 2 of the Critical Thinking Assignment here is the link for GeoGebra: https://www.geogebra.org/calculator.

Part 1

Creating a Related Rates Animation For this Critical Thinking Assignment, you will be creating an animation that models a related rates problem using GeoGebra.

1.0: Complete the following steps: 1. Learn how to create animations in GeoGebra here: https://wiki.geogebra.org/en/Animation

2. Select a related rates problem from all even-numbered exercises 6 – 40 of Section 4.1 in Calculus, Volume 1.

3. Before solving the problem, model the way that the variables are changing by creating a GeoGebra animation.

4. Save your GeoGebra work as a .pdf file for submission. 5. Solve the related rates problem you selected.

1.2: Based on your work in 1.0, discuss the following:

1. Discuss why you chose the related rates problem and what challenges you faced in trying to solve it. 2. Discuss the domain and range of the function. Do these values make sense in this context?

3. How exact is your model in showing how the variables from the problem are changing in relation to each other?

4. What are the limitations in trying to visually check your answer using the animation? Would there have been a way to determine the answer only by using your animation?

5. Discuss any challenges you faced when creating the animation.

6. Discuss any new information about the problem that you discovered by creating an animation to solve it.

7. Provide at least two other real-world situations that involve related rates and respond to the following: a. What common characteristics do the real-world scenarios you chose share? b. What did you look for in the way that the real-world scenario can be modeled? Requirements: You must submit two files for this assignment. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in 1.0. 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 2- to 3-page narrative paper, written in APA format, associated with the situation described in Part II. Specific requirements for the paper are provided below: a. Your paper should be 2-3 pages in length (not counting the title page and references page) and should cite and integrate at least two credible outside sources. The CSUGlobal Library is a great place to find resources. Your textbook is a credible resource. b. Include a title page, introduction, body, conclusion, and a reference page. i. 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. ii. 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. iii. 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. c. Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables, graphs, etc.)

Part 2

Part I: Complete the following steps:

1. Read Example 4.34 in Section 4.7 of Calculus, Volume 1.

2. Consider the following scenario:

A lifeguard is at point A of a circular pool with diameter 40 m. He must reach someone who is drowning

on the exact opposite side of the pool, at position C. The lifeguard swims with a speed v = 3 m/s from

point A to point B, and then runs around the pool from point B to point C at speed w = 9 m/s. You will

find an image representation in your Module 6 area in your course.

a. Find a function that measures the total amount of time it takes to reach the drowning person as

a function of the swim angle, 𝜃𝜃 expressed in radians.

b. Find at what angle 𝜃𝜃, in radians, the lifeguard should swim to reach the drowning person in the

least amount of time.

c. What is the domain of the function you created in part (a)?

Part II: Based on your work in Part I, discuss the following:

1. How do you know that the function you created in Part I has a maximum and minimum value?

2. Discuss how your answers to Part I would be affected if the diameter of the pool increased.

3. For what running speed would it be faster to swim the entire time? What angle would

correspond to this scenario?

4. For what angle, 𝜃𝜃, would it take the longest to reach the drowning person?

5. Suppose the pool was rectangular. Respond to the following:

a. Does it still make sense to parameterize using ? Why or why not?

i. If not, what parameter would you use?

ii. If so, how does the parameterization change?

b. Set up, but do not solve, this problem with a rectangular pool.

6. Answer the following questions that reference Example 4.34:

a. How do we know that the function T(x) has a maximum and minimum?

b. What restrictions are there on what the domain of T can be in this scenario?

c. Elaborate, in your own words, on why we must evaluate T(0) and T(6).

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 2- to 3-page narrative paper, written in APA format, associated with the

situation described in Part II. Specific requirements for the paper are provided below:

a. Your paper should be 2-3 pages in length (not counting the title page and references page) and

should 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.

b. Include a title page, introduction, body, conclusion, and a reference page.

i. 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.

ii. 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.

iii. 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.

c. Include any tables of data or calculations, calculated values, and/or graphs referenced in the

paper. (Note: The minimum required length excludes any tables, graphs, etc.)