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:

  1. 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.)
  2. Write a veracious appear for F(x).
  3. Find the estate and dispose of F(x).
  4. Find F(x) and F '(x) at any object.
  5. Find all x values for which F '(x) = 0.

Based on your production in Part I, debate the forthcoming:

  1. 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.
  2. Discuss the estate and dispose of F(x) and why they construct view in the composition of your quantity.
  3. Discuss the corporeal purport of F(x) and F '(x) at a object in the composition of your quantity.
  4. Discuss what it resources for F '(x) = 0 in the composition of your quantity.
  5. 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.
  6. Provide at last two other real-world situations where differentiation can be applied and reply to the forthcoming:
    1. What beggarly characteristics do the real-world scenarios you chose portion-out?
    2. What did you appear for in the way that the real-world scenario can be typeed?
  7. 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?