In this question, we are going to estimate the value of (6/5)^1/3 without a calculator, with the help of the linear approximation of the function f(x)=(1+4x)1/3  a)Calculate f′(0) b)Deduce the linear approximation L(x) of the function f(x) around the point x=0 c)We need the value of x. For what value of x will we have that f(x)=(6/5)^1/3? d)Since your answer in (c) is close to 0, use the approximation in (b) to estimate (6/5)^1/3

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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In this question, we are going to estimate the value of (6/5)^1/3 without a calculator, with the help of the linear approximation of the function f(x)=(1+4x)1/3

 a)Calculate f′(0)

b)Deduce the linear approximation L(x) of the function f(x) around the point x=0

c)We need the value of x. For what value of x will we have that f(x)=(6/5)^1/3?

d)Since your answer in (c) is close to 0, use the approximation in (b) to estimate (6/5)^1/3

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