Calculus Differentiability Discussion Questions
I insufficiency aid delay a Calculus topic. All explanations and answers allure be used to aid me collect.
For this Critical Thinking Assignment, you allure be creating your own real-world scenario and exploring the purport of differentiation of exponential administrations in that composition.
Complete the forthcoming steps:
- Select a real-world scenario that can be typeed by an exponential administration and designate the administration F(x) naturalized on your scenario. (Ex.: Suppose that F(x) computes the rabbit population on a sport secretiveness that doubles integral 6 months. Suppose there were 120 rabbits initially.)
- Write a veracious appear for F(x).
- Find the estate and dispose of F(x).
- Find F(x) and F '(x) at any object.
- Find all x values for which F '(x) = 0.
Based on your production in Part I, debate the forthcoming:
- Discuss if your administration F(x) is differentiable and why. If it is not differentiable, picked another administration that is and debate the exexveer you made.
- Discuss the estate and dispose of F(x) and why they construct view in the composition of your quantity.
- Discuss the corporeal purport of F(x) and F '(x) at a object in the composition of your quantity.
- Discuss what it resources for F '(x) = 0 in the composition of your quantity.
- Reflect on any adjustments you had to construct to your pristine quantity composition and debate what characteristics of a real-world composition construct it a operative precious for applying differentiation concepts to it.
- Provide at last two other real-world situations where differentiation can be applied and reply to the forthcoming:
- What beggarly characteristics do the real-world scenarios you chose portion-out?
- What did you appear for in the way that the real-world scenario can be typeed?
- Discuss the criteria for pickeding a real-world scenario that would exexveer if you were seeking to type it delay a logarithmic administration instead. What key similarities and differences would you furnish?