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1. Knowing that the sixth root of 64 is 2, estimate the sixth root of 68 by using the tangent line to the sixth root function (y = x6) at (64, 2) as an approximation to the function itself. (Remember that, when evaluating a fractional root without a calculator, take the root first and then apply the exponentiation. So, for example, to evaluate 275/3, take the cube root of 27 first to get 3, then raise that to the fifth power to get 243. That's as opposed to raising 27 to the fifth power (14,348,907) and then trying to figure out that its cube root is 243.)

1. Knowing that the sixth root of 64 is 2, estimate the sixth root of 68 by using the tangent line to the sixth root function (y = x6) at (64, 2) as an approximation to the function itself. (Remember that, when evaluating a fractional root without a calculator, take the root first and then apply the exponentiation. So, for example, to evaluate 275/3, take the cube root of 27 first to get 3, then raise that to the fifth power to get 243. That's as opposed to raising 27 to the fifth power (14,348,907) and then trying to figure out that its cube root is 243.)

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. Knowing that the sixth root of 64 is 2, estimate the sixth root of 68 by using the tangent line to the sixth root function (y = x/6) at (64, 2) as an approximation to the function itself. (Remember that, when evaluating a fractional root without a calculator, take the root first and then apply the exponentiation. So, for example, to evaluate 275/3, take the cube root of 27 first to get 3, then raise that to the fifth power to get 243. That's as opposed to raising 27 to the fifth power (14,348,907) and then trying to figure out that its cube root is 243.)
Transcribed Image Text:1. Knowing that the sixth root of 64 is 2, estimate the sixth root of 68 by using the tangent line to the sixth root function (y = x/6) at (64, 2) as an approximation to the function itself. (Remember that, when evaluating a fractional root without a calculator, take the root first and then apply the exponentiation. So, for example, to evaluate 275/3, take the cube root of 27 first to get 3, then raise that to the fifth power to get 243. That's as opposed to raising 27 to the fifth power (14,348,907) and then trying to figure out that its cube root is 243.)
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