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Find the equation of the tangent line to

Find the equation of the tangent line to

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
### Exercise 3: Linear Approximation In this problem, you will use a linear approximation to determine the value of \((1.1)^{4/3}\). #### (a) Function and Value of \(x\) **Question:** What function do you want to approximate here, and at what value of \(x\)? - \(f(x) =\) - at \(x =\) #### (b) Anchor Point **Question:** What’s a number close to \(x\) where you know the value of this function? This number should be your “anchor point” \(a\). #### (c) Tangent Line Equation **Question:** Find the equation of the tangent line to \(f(x)\) at \(x = a\). #### (d) Approximate Value **Task:** Plug the value of \(x\) from part (a) into your equation for the tangent line. This is the approximate value of \((1.1)^{4/3}\). #### (e) Calculate Error and Percent Error **Task:** All of the above could (in theory) be done without a calculator. Now use a calculator to compute the actual value of \((1.1)^{4/3}\). What is the error? What is the percent error?
Transcribed Image Text:### Exercise 3: Linear Approximation In this problem, you will use a linear approximation to determine the value of \((1.1)^{4/3}\). #### (a) Function and Value of \(x\) **Question:** What function do you want to approximate here, and at what value of \(x\)? - \(f(x) =\) - at \(x =\) #### (b) Anchor Point **Question:** What’s a number close to \(x\) where you know the value of this function? This number should be your “anchor point” \(a\). #### (c) Tangent Line Equation **Question:** Find the equation of the tangent line to \(f(x)\) at \(x = a\). #### (d) Approximate Value **Task:** Plug the value of \(x\) from part (a) into your equation for the tangent line. This is the approximate value of \((1.1)^{4/3}\). #### (e) Calculate Error and Percent Error **Task:** All of the above could (in theory) be done without a calculator. Now use a calculator to compute the actual value of \((1.1)^{4/3}\). What is the error? What is the percent error?
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