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4. Let f(x) = (a) Suppose we start at z = 2 (so this is the "anchor point" a), and make a change in r of Ar = 0.3. Use the "short form" of the linear approximation formula, Af x f'(a) · Ar, to approximate the corresponding change in f (that is, Af). (b) The eract value of Af (that you approximated in part (a)) is a difference of two values of f. Using a calculator, compute this exact value of Af. (Hint: What two r values do you need to plug in?) (c) Compute the error and the percentage error between your approximation of Aƒ and the actual value.

4. Let f(x) = (a) Suppose we start at z = 2 (so this is the "anchor point" a), and make a change in r of Ar = 0.3. Use the "short form" of the linear approximation formula, Af x f'(a) · Ar, to approximate the corresponding change in f (that is, Af). (b) The eract value of Af (that you approximated in part (a)) is a difference of two values of f. Using a calculator, compute this exact value of Af. (Hint: What two r values do you need to plug in?) (c) Compute the error and the percentage error between your approximation of Aƒ and the actual value.

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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1 4. Let f(2) = (a) Suppose we start at z = 2 (so this is the "anchor point" a), and make a change in r of Ar = 0.3. Use the "short form" of the linear approximation formula, Af x f'(a) · Ar, to approximate the corresponding change in f (that is, Af). (b) The eract value of Af (that you approximated in part (a)) is a difference of two values of f. Using a calculator, compute this exact value of Af. (Hint: What two r values do you need to plug in?) (c) Compute the error and the percentage error between your approximation of Af and the actual value.
Transcribed Image Text:1 4. Let f(2) = (a) Suppose we start at z = 2 (so this is the "anchor point" a), and make a change in r of Ar = 0.3. Use the "short form" of the linear approximation formula, Af x f'(a) · Ar, to approximate the corresponding change in f (that is, Af). (b) The eract value of Af (that you approximated in part (a)) is a difference of two values of f. Using a calculator, compute this exact value of Af. (Hint: What two r values do you need to plug in?) (c) Compute the error and the percentage error between your approximation of Af and the actual value.
Expert Solution
Step 1

Here, the given function is f(x)=11+x3.

Differentiate with respect to x,

f'(x)=-3x2(1+x3)2

Now, at x=2, we get 

f'(2)=-3(2)2(1+23)2=-427

(a)

Using ∆f≈f'(a)·∆x and ∆x=0.3, we get

∆f≈-427·0.3=-245

 

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