1.) p(x)=3x^2-x+8, million dollars is a company’s profit, x years after 2000, 0≤x≤10Find the derivative of p(x) using the limit definition (algebraic method) of the derivative.Remember to start with the general definition of a derivative and show ALL steps involved in simplifying until you can finally evaluate the limit.Check that you actually have included a step that shows the limit of a completely simplified algebraic expression and that the next step shows the limit of that algebraic expression (but does not have limit notation).Check that you start each step (after the initial step) with an equals sign, and that the limit notation is included in every step before the limit calculation.2.) Find P'(5) 3.) Write a sentence of interpretation for P'(5) 4.) Find the percentage rate of change in the company’s profit in 2005, Write the answer rounded to three decimal places. 5.)Verify the units of the previous question.A.) million dollarsB.) % per yearC.) million dollars per yearD.) year 6.) Write a sentence of interpretation for the percentage rate of change in the company’s profit in 2005.

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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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1.) p(x)=3x^2-x+8, million dollars is a company’s profit, x years after 2000, 0≤x≤10

Find the derivative of p(x) using the limit definition (algebraic method) of the derivative.

Remember to start with the general definition of a derivative and show ALL steps involved in simplifying until you can finally evaluate the limit.
Check that you actually have included a step that shows the limit of a completely simplified algebraic expression and that the next step shows the limit of that algebraic expression (but does not have limit notation).
Check that you start each step (after the initial step) with an equals sign, and that the limit notation is included in every step before the limit calculation.

2.) Find P'(5)

3.) Write a sentence of interpretation for P'(5)

4.) Find the percentage rate of change in the company’s profit in 2005, Write the answer rounded to three decimal places.

5.)

Verify the units of the previous question.

A.) million dollars

B.) % per year

C.) million dollars per year

D.) year

6.) Write a sentence of interpretation for the percentage rate of change in the company’s profit in 2005.

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