Describe in detail what you need	in English language make me an instruction about giving a project in Calculus 1 to 15 students by pair /by triad about application of derivatives.
How many pages	1

Project Assignment: Application of Derivatives

Introduction

In this project, you will explore the practical applications of derivatives in various fields. This assignment is designed for students enrolled in Calculus 1, and the objective is to enhance your understanding of derivatives by applying them to real-world problems. You will work in pairs or triads, encouraging collaboration and deeper learning.

Project Details

Group Formation

• Each group will consist of two to three students. You can choose your group members, but please ensure that the final count does not exceed fifteen students in total.

Project Topic Selection

Each group will select one of the following topics to explore the application of derivatives:

1. Economics: Investigate how derivatives can be used to find maximum profit or minimum cost for a business.
2. Physics: Examine the concept of velocity and acceleration using the first and second derivatives of a position function.
3. Biology: Analyze population growth rates and the concept of logistic growth using derivatives.
4. Engineering: Explore the application of derivatives in optimizing design parameters for structures or mechanical systems.
5. Medicine: Study how derivatives can predict the spread of diseases based on real-world data.

Deliverables

Your group will be required to submit both a written report and a presentation. The specifics of each deliverable are outlined below:

Written Report

• Length: The report should be 3-5 pages long, excluding title page and references.
• Format: Use a standard format with the following sections:
  • Title Page: Include the title of your project, group members' names, course name, and submission date.
  • Introduction: Briefly introduce the application of derivatives you will be discussing.
  • Analysis: Delve into the mathematical concepts related to your topic, using derivatives to explain your findings.
  • Real-World Application: Discuss how the theory applies to real-world scenarios with examples.
  • Conclusion: Summarize your findings and reflect on the importance of derivatives in your chosen field.
  • References: Include a list of resources used for research in APA format.

Presentation

• Duration: Your group will present for 10-15 minutes during the final week of class.
• Format:
  • Use PowerPoint or another presentation tool.
  • Clearly present your main findings, focusing on key concepts and examples.
  • Engage your classmates with questions to stimulate discussion.

Timeline

• Week 1: Form groups and select topics.
• Week 2: Conduct research and begin drafting the written report.
• Week 3: Complete the report and begin developing the presentation.
• Week 4: Rehearse presentations and finalize all deliverables.
• Final Week: Present your findings to the class.

Assessment Criteria

Grades will be based on the following criteria:

1. Understanding of Derivatives: Clarity in explaining how derivatives are applied in your chosen topic.
2. Depth of Analysis: Quality of mathematical analysis and use of real-world examples.
3. Quality of Reports: Clarity, organization, adherence to formatting, and academic integrity in citations.
4. Presentation Skills: Ability to communicate ideas effectively and engage the audience.

Conclusion

This project will enable you to gain a deeper appreciation of derivatives' significance beyond theoretical frameworks. By collaborating with your peers and conducting thorough research, you will be able to see the direct impact of calculus in various fields. We look forward to your innovative ideas and findings. Happy learning!