I need part 2 and 3 pls! Application - ForestryA team of researchers finds that there is a relationship between the overall health of a forest they're studying and thepopulation of a certain beetle which feeds on the bark of old-growth trees. Due to the warming climate, the beetles arenow able to reproduce one more time per year than they previously did, exacerbating the stress caused by the drought13x³ +67of the past few seasons. They use the function f(x)to model the relationship between the two populations,.6x5 +39where x is in tens of thousands of beetles and f is in thousands of trees. They note that there is a beneficialcontribution to the ecosystem as a whole for a smaller population of the beetles, but that the number of healthy treessharply declines as the beetle population rises too much.-1. Graph f(x) using technology.a. What appears to be the maximum number of healthy trees, to the nearest thousand? What is the estimatedbeetle population corresponding to this, to the nearest ten thousand?b. What is the slope of the tangent line to the graph of f (x) at the point corresponding to the maximum number ofhealthy trees (and the optimal population of beetles)? How do you know?c. How can f¹ (x) help us find the actual coordinates of the point we just estimated? (Don't actually find it yet, justdescribe how f¹ (x) is useful for answering this question, what steps you would take to do this and why.)2. Write down the limit definition of ƒ¹ (x). Do not actually solve this limit.a. Would you want to use the limit definition of the derivative to find ƒ' (x)? Why or why not?b. Use the differentiation rules we learned in this unit to find f¹ (x), describing which rules you're using at eachstep and telling me the story of your process.3. Use ƒ' (x) to find the point you described (you can use technology to find it, just please tell me what you're havingthe technology do for you).4. Find the equation of the tangent line to the graph of ƒ (x) at this point, telling me the story of your process.5. Use the equation of the tangent line to estimate the tree population when the beetle population is 30,000, tellingme the story of your process.

Answered: Image /qna-images/answer/67c40309-67ba-4736-9fb6-8b861e9c3ce2.jpg

2. Write down the limit definition of f (x). Do not actually solve this limit. a. Would you want to use the limit definition of the derivative to find f (x)? Why or why not? b. Use the differentiation rules we learned in this unit to find f (x), describing which rules you're using at each step and telling me the story of your process. 3. Use f'(x) to find the point you described (you can use technology to find it, just please tell me what you're having the technology do for you).

2. Write down the limit definition of f (x). Do not actually solve this limit. a. Would you want to use the limit definition of the derivative to find f (x)? Why or why not? b. Use the differentiation rules we learned in this unit to find f (x), describing which rules you're using at each step and telling me the story of your process. 3. Use f'(x) to find the point you described (you can use technology to find it, just please tell me what you're having the technology do for you).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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