5Let f(x) =2л-5хThen the slope of the tangent line to the graph of y = f(x) at the point (T,5Злis the limit as x tends toof the following expressionThe value of this limit isIt follows that the equation of the tangent line is y =

The slope of the tangent line at any point x0 is given by the limit as x tends to x0 of the…

Answered: 5 Let f(x) = 2л-5х Then the slope of…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 4T

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Your job is to find some shortcuts for taking derivatives. For example, if the function is of the form y = c, where c is a constant, then you know the graph is a horizontal line, with a slope of zero, and you don't have to even go through the limit gyrations to get the derivative. Do some experimenting with the limit definition on some easy functions to see what you get. When you post a shortcut, you must also post a good portion of the algebraic (or geometric) argument that supports it. No numerical or graphical (calculator) approximations will count as justification — you need to argue with algebra or geometry.
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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.)…
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5 Let f(x) = 2л-5х Then the slope of the tangent line to the graph of y = f(x) at the point (T, 5 Зл is the limit as x tends to of the following expression The value of this limit is It follows that the equation of the tangent line is y =