Calculus Differentiability Discussion Questions Assignment
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Calculus Differentiability Discussion Questions Assignment
For this Critical Thinking Assignment, you will be creating your own real-world scenario and exploring the meaning of differentiation of exponential functions in that context.
Complete the following steps:
Select a real-world scenario that can be modeled by an exponential function and define the function F(x) based on your
scenario. (Ex.: Suppose that F(x) computes the rabbit population on a game reserve that doubles every 6 months.
Suppose there were 120 rabbits initially.)
Write a mathematical expression for F(x).
Find the domain and range of F(x).
Find F(x) and F ‘(x) at any point.
Find all x values for which F ‘(x) = 0.
Based on your work in Part I, discuss the following:
Discuss if your function F(x) is differentiable and why. If it is not differentiable, select another function that is and discuss the change you made.
Discuss the domain and range of F(x) and why they make sense in the context of your problem.
Discuss the physical meaning of F(x) and F ‘(x) at a point in the context of your problem.
Discuss what it means for F ‘(x) = 0 in the context of your problem.
Reflect on any adjustments you had to make to your original problem context and discuss what characteristics of a real-world context make it a valid choice for applying differentiation concepts to it.
Provide at least two other real-world situations where differentiation can be applied and respond to the following:
What common characteristics do the real-world scenarios you chose share?
What did you look for in the way that the real-world scenario can be modeled?
Discuss the criteria for selecting a real-world scenario that would change if you were seeking to model it with a logarithmic function instead. What key similarities and differences would you find?
RUBRIC
Excellent Quality
95-100%
Introduction 45-41 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Literature Support
91-84 points
The background and significance of the problem and a clear statement of the research purpose is provided. The search history is mentioned.
Methodology
58-53 points
Content is well-organized with headings for each slide and bulleted lists to group related material as needed. Use of font, color, graphics, effects, etc. to enhance readability and presentation content is excellent. Length requirements of 10 slides/pages or less is met.
Average Score
50-85%
40-38 points
More depth/detail for the background and significance is needed, or the research detail is not clear. No search history information is provided.
83-76 points
Review of relevant theoretical literature is evident, but there is little integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are included. Summary of information presented is included. Conclusion may not contain a biblical integration.
52-49 points
Content is somewhat organized, but no structure is apparent. The use of font, color, graphics, effects, etc. is occasionally detracting to the presentation content. Length requirements may not be met.
Poor Quality
0-45%
37-1 points
The background and/or significance are missing. No search history information is provided.
75-1 points
Review of relevant theoretical literature is evident, but there is no integration of studies into concepts related to problem. Review is partially focused and organized. Supporting and opposing research are not included in the summary of information presented. Conclusion does not contain a biblical integration.
48-1 points
There is no clear or logical organizational structure. No logical sequence is apparent. The use of font, color, graphics, effects etc. is often detracting to the presentation content. Length requirements may not be met
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Calculus Differentiability Discussion Questions Assignment