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Rope-a-Dope A company manufactures rope, and the total cost of producing r feet of rope is C(r) dollars. You know that C(2000) = 800 and C"(2000) = 0.35. Write the point-slope form of the equation of the tangent line to the graph of the function. Use your tangent line equation to derive the linearization of C(r) at r = 2000. Use your linearization to estimate C(2100).

Rope-a-Dope A company manufactures rope, and the total cost of producing r feet of rope is C(r) dollars. You know that C(2000) = 800 and C"(2000) = 0.35. Write the point-slope form of the equation of the tangent line to the graph of the function. Use your tangent line equation to derive the linearization of C(r) at r = 2000. Use your linearization to estimate C(2100).

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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Rope-a-Dope A company manufactures rope, and the total cost of producing r feet of rope is C(r) dollars. You know that C(2000) = 800 and C"(2000) = 0.35. Write the point-slope form of the equation of the tangent line to the graph of the function. Use your tangent line equation to derive the linearization of C(r) at r= 2000. Use your linearization to estimate C(2100). What else would you need to know about the function at r= 2000 to determine if your approximation was an over estimate or an under estimate?
Transcribed Image Text:Rope-a-Dope A company manufactures rope, and the total cost of producing r feet of rope is C(r) dollars. You know that C(2000) = 800 and C"(2000) = 0.35. Write the point-slope form of the equation of the tangent line to the graph of the function. Use your tangent line equation to derive the linearization of C(r) at r= 2000. Use your linearization to estimate C(2100). What else would you need to know about the function at r= 2000 to determine if your approximation was an over estimate or an under estimate?
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